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Call number: | 9783319508535:ONLINE Show nearby items on shelf |
Title: | Algebra II Textbook for Students of Mathematics |
Author(s): |
Alexey L Gorodentsev |
Date: | 2017 |
Size: | 1 online resource (XV, 370 p. 155 illus., 2 illus. in color p.) |
Contents: | §1Tensor Products -- §2 Tensor Algebras -- §3 Symmetric Functions -- §4 Calculus of Arrays, Tableaux, and Diagrams -- §5 Basic Notions of Representation Theory -- §6 Representations of Finite Groups in Greater Detail -- §7 |
Representations of Symmetric Groups -- §8 sl_2-Modules -- §9 Categories and Functors -- §10 Extensions of Commutative Rings -- §11 Affine Algebraic Geometry -- §12 Algebraic Manifolds -- §13 Algebraic Field Extensions -- §14 Examples | |
of Galois Groups -- References -- Hints to Some Exercises -- Index | |
ISBN: | 9783319508535 |
Series: | eBooks |
Series: | Springer eBooks |
Series: | Springer 2017 package |
Keywords: | Mathematics , Algebra , Mathematics , Algebra |
Availability: | Click
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Call number: | SPRINGER-2016-9783319388557:ONLINE Show nearby items on shelf |
Title: | Multiplicative Ideal Theory and Factorization Theory Commutative and Non-commutative Perspectives |
Author(s): | |
Date: | 2016 |
Size: | 1 online resource (407 p.) |
Note: | 10.1007/978-3-319-38855-7 |
Contents: | Multiplicative Ideal Theory in Non-commutative Rings (E. Akalan, H. Marubayashi) -- About number fields with Pólya group of order ≤ 2 (D. Adam, J.-L. Chabert) -- The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmet ic Combinatorics (K. Cziczler, M. Domokos, A. Geroldinger) -- Ring and semigroup constructions (M. D'Anna) -- New Distinguished Classes of Spectral Spaces (C.A. Finocchiaro, M. Fontana, D. Spirito) -- Relative polynomial closure and monadically Krull mono ids of integer-valued polynomials (S. Frisch).-An overview of the computational aspects of nonunique factorization invariants (P.A. García-Sánchez).-Arithmetic of Mori domains and monoids: The global case (F. Kainrath) -- Prüfer Domains of Integer-Valu ed Polynomials (K.A. Loper, M. Syvuk) -- Lobal Properties of Integral Domains (T.G. Lucas) -- Topological aspects of irredundant intersections of ideals and valuation rings (B. Olberding) -- Noetherian semigroup algebras and beyond (J. Okniński) |
-- Idempotent pairs and PRINC domains (G. Peruginelli, L. Salce, P. Zanardo) -- Some recent results and open problems on sets of lengths of Krull monoids with finite class group (W.A. Schmid) -- Factorizations of elements in noncommutative rings: A survey (D. Smertnig) | |
ISBN: | 9783319388557 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Springer Proceedings in Mathematics & Statistics: 170 |
Keywords: | Mathematics , Algebraic geometry , Associative rings , Rings (Algebra) , Commutative algebra , Commutative rings , Group theory , Number theory , Mathematics , Commutative Rings and Algebras , Number Theory , Group Theory and Generalizations , Associative Rings and Algebras , Algebraic Geometry |
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Call number: | SPRINGER-2016-9783319267654:ONLINE Show nearby items on shelf |
Title: | On the Geometry of Some Special Projective Varieties |
Author(s): |
Francesco Russo |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (232 p.) |
Note: | 10.1007/978-3-319-26765-4 |
Contents: | Preface.-Introduction -- 1.Tangent cones, tangent spaces, tangent stars secant, tangent and tangent star varieties to an algebraic variety -- 2.Basics of Deformation Theory of Rational Curves on Projective Varieties -- 3.Fulton-Hansen Connectedness Theorem, Scorza Lemma and their applications to projective geometry -- 4.Local quadratic entry locus manifolds and conic connected manifolds -- 5.Hartshorne Conjectures and Severi varieties -- 6.Varieties n-covered by curves of a fixed degree and the XJC -- 7. Hypersurfaces with vanishing hessian.-Bibliography |
ISBN: | 9783319267654 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes of the Unione Matematica Italiana: 18 |
Keywords: | Mathematics , Algebraic geometry , Commutative algebra , Commutative rings , Geometry , Mathematics , Algebraic Geometry , Commutative Rings and Algebras , Geometry |
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Call number: | SPRINGER-2016-9783319264370:ONLINE Show nearby items on shelf |
Title: | Minimal Free Resolutions over Complete Intersections |
Author(s): |
David Eisenbud |
Date: | 2016 |
Edition: | 1st ed. 2016 |
Size: | 1 online resource (107 p.) |
Note: | 10.1007/978-3-319-26437-0 |
ISBN: | 9783319264370 |
Series: | eBooks |
Series: | SpringerLink (Online service) |
Series: | Springer eBooks |
Series: | Lecture Notes in Mathematics: 2152 |
Keywords: | Mathematics , Algebraic geometry , Category theory (Mathematics) , Homological algebra , Commutative algebra , Commutative rings , Physics , Mathematics , Commutative Rings and Algebras , Algebraic Geometry , Category Theory, Homological Algebra , Theoretical, Mathematical and Computational Physics |
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Call number: | SPRINGER-2014-9783319032122:ONLINE Show nearby items on shelf |
Title: | Manis Valuations and Prfer Extensions II [electronic resource] |
Author(s): |
Manfred Knebusch Tobias Kaiser |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume is a sequel to Manis Valuation and Prfer Extensions I, LNM1791. The Prfer extensions of a commutative ring A are roughly those commutative ring extensions R / A,where commutative algebra is governed by Manisvaluations on R with integral v alues on A. These valuations then turn out to belong to the particularly amenable subclass of PM (=Prfer-Manis) valuations. While in Volume I Prfer extensions in general and individual PM valuationswere studied, now the focus is on families of PM valuatio ns. One highlight is the presentation of a very general and deep approximation theorem for PM valuations, going back to Joachim Grters work in 1980, a far-reaching extensionof the classical weak approximation theorem in arithmetic. Another highlight is a theory of so called Kronecker extensions, where PM valuations are put to use in arbitrary commutative ring extensions in a way that ultimatelygoes back to the work of Leopold Kronecker |
Contents: | Overrings and PM |
Spectra | |
Approximation Theorems | |
Kronecker extensions and star operations | |
Basics on Manis valuations and Prufer extensions | |
Multiplicative ideal theory | |
PM | |
valuations and valuations of weaker type | |
Overrings and PM | |
Spectra | |
Approximation Theorems | |
Kronecker extensions and star operations | |
Appendix | |
References | |
Index | |
ISBN: | 9783319032122 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2103 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2014-9783319015897:ONLINE Show nearby items on shelf |
Title: | Non-commutative Multiple-Valued Logic Algebras [electronic resource] |
Author(s): |
Lavinia Corina Ciungu |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras a subject which has attracted much interest in the past few years because of its impact on informationscience, artificial intelli gence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices,pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebrasin thatalgebraic structures can be developed into fuzzy logics which connect quantum mechanics,mathematical logic, probability theory, algebra and soft computing. Written in a c lear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well asresearchers in mathematical logic and theoretical computer science |
Contents: | Pseudo |
BCK algebras | |
Pseudo | |
hoops | |
Residuated lattices | |
Other non | |
commutative multiple | |
valued logic algebras | |
Classes of non | |
commutative residuated structures | |
States on multiple | |
valued logic algebras | |
Measures on pseudo | |
BCK algebras | |
Generalized states on residuated structures | |
Pseudo | |
hoops with internal states | |
ISBN: | 9783319015897 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Logic, Symbolic and mathematical , Distribution (Probability theory) |
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Call number: | SPRINGER-2014-9783319003337:ONLINE Show nearby items on shelf |
Title: | Quantum Potential: Physics, Geometry and Algebra [electronic resource] |
Author(s): |
Ignazio Licata Davide Fiscaletti |
Date: | 2014 |
Publisher: | Cham : Springer International Publishing : Imprint: Springer |
Size: | 1 online resource |
Note: | Recently the interest in Bohm realist interpretation of quantum mechanics has grown. The important advantage of this approach lies in the possibility to introduce non-locality ab initio, and not as an unexpected host. Inthis bookthe authors give a de tailed analysis of quantum potential, the non-locality term and its role in quantum cosmology and information. The different approaches to the quantum potential are analysed, starting from the originalattempt to introduce a realism of particles trajectori es (influenced by de Broglies pilot wave) to the recent dynamic interpretation provided by Goldstein, Durr, Tumulka and Zangh, and the geometrodynamic picture, with suggestionabout quantum gravity. Finally we focus on the algebraic reading of Hiley and Bi rkbeck school, that analyse the meaning of the non-local structure of the world, bringing important consequences for the space, time and informationconcepts |
Contents: | From the Contents: Quantum Potential |
The Quantum Potential in Schrdinger Equation | |
The Pilot Wave Theory | |
Particles trajectories as the foundation of Bohms mechanics: the nutshell of Drr, Goldstein, Tumulka and Zangh | |
Non | |
Commutative Quantum Geometry and the Algebraic Approach to Non | |
Locality | |
Quantum potential in particle and field theory models | |
Klein Gordon Equation and Bertoldi | |
Faraggi | |
Matone Theory | |
The quantum potential in Bohms approach to the Dirac relativistic quantum mechanics | |
Quantum Potential in Curved Space Field Theory | |
ISBN: | 9783319003337 |
Series: | eBooks |
Series: | SpringerLink |
Series: | SpringerBriefs in Physics, 2191-5423 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Quantum theory |
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Call number: | SPRINGER-2014-9781493909254:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Recent Advances in Commutative Rings, Integer-Valued Polynomials, and Polynomial Functions |
Author(s): |
Marco Fontana Sophie Frisch Sarah Glaz |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | This volume presents a multi-dimensional collection of articles highlighting recent developments in commutative algebra. It also includes an extensive bibliography and lists a substantial number of open problems that point tofuture directions of rese arch in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics andresearch methods include Noetherian and non- Noetheri an ring theory as well as integer-valued polynomials and functions. Specific topics include: Homological dimensions of Prfer-like rings Quasi complete rings Total graphs of rings Properties of prime ideals over various rings Bases for integer-valued p olynomials Boolean subrings The portable property of domains Probabilistic topics inIntn(D) Closure operations in Zariski-Riemann spaces of valuation domains Stability of domains Non-Noetherian grade Homotopy in integer-valued polynomials Localiza tions of global propertiesof rings Topics in integral closure Monoids and submonoids of domains The book includes twenty articles written by many of the most prominent researchers in the field. Most contributions are authored by attendees ofthe conferen ce in commutative algebra held at the Graz University of Technology in December 2012. There is also a small collection of invited articles authored by those who did not attend the conference. Following the model of the Grazconference, the volume contains a number of comprehensive survey articles along with related research articles featuring recent results that have not yet been published elsewhere |
Contents: | Preface |
Weak global dimension of Prfer | |
like rings (K. Adarbeh, S | |
E. Kabbaj) | |
Quasi | |
complete semilocal rings and modules (D.D. Anderson) | |
On the total graph of a ring and its related graphs: A survey (A. Badawi) | |
Prime ideals in polynomials and power series rings over Noetherian domains | |
Integer | |
valued polynomials: Looking for regular bases (J | |
L. Chabert) | |
On Boolean subrings of rings (I. Chajda, G. Eigenthaler) | |
On a new class of integral domains with the portable property (D.E. Dobbs, G. Picavet, M. Picavet | |
L'Hermitte) | |
The probability that Intn(D) is free (J. Elliott | |
ISBN: | 9781493909254 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology |
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Call number: | SPRINGER-2014-9781493906260:ONLINE Show nearby items on shelf |
Title: | Connections Between Algebra, Combinatorics, and Geometry [electronic resource] |
Author(s): |
Susan M Cooper Sean Sather-Wagstaff |
Date: | 2014 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics,and Geometry contains lecture notes, alongwith exercises andsolution s, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participatein the companion Special Session on Interactions B etween Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 23, 2012, and the meeting Further ConnectionsBetween Algebra and Geometry, which was held at the North Dakota State Universit y, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutativealgebra, secant varieties, and fat points and symbolic powers. Itwill serve asausefulresourcefor gra duate students andresearchers who wish toexpand their knowledge of commutative algebra, algebraicgeometry,combinatorics, and the intricacies of their intersection. |
Contents: | Preface |
Differential Graded Commutative Algebra | |
Secant Varieties | |
Fat Points and Symbolic Powers | |
An Introduction to Stanley | |
Reisner Rings | |
Combinatorial Resolutions | |
Geometric Properties of the Tor Algebra Structure for Trivariate Monomial Ideals | |
Interactions Between Linear Algebra and Algebraic Geometry | |
Fat Points | |
Primary Decomposition of Certain Permanental Ideals | |
ISBN: | 9781493906260 |
Series: | eBooks |
Series: | SpringerLink |
Series: | Springer Proceedings in Mathematics & Statistics, 2194-1009 : v76 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2013-9783642394850:ONLINE Show nearby items on shelf |
Title: | Algebras, Quivers and Representations [electronic resource] : The Abel Symposium 2011 |
Author(s): |
Aslak Bakke Buan Idun Reiten yvind Solberg |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas ofmathematics like commutati ve algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systemsand triangulated categories. In addition, it in cludes contributions on further developments in representation theory of quivers and algebras. Algebras, Quivers and Representations is targeted at researchers and graduate students inalgebra, representation theory and triangulated categories |
Note: | Springer eBooks |
Contents: | C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions |
L. Avramov: (Contravariant) Koszul duality for DG algebras | |
R. Buchweitz: The fundamental group of a morphism in a triangulated category | |
K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras | |
D. Happel: Algebras of finite global dimension | |
K. Igusa (with G. Todorov): Continuous Frobenius categories | |
D.A. Jorgensen: Triangle functors from generic hypersurfaces | |
Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian | |
H. Krause: Mo | |
ISBN: | 9783642394850 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia, 2193-2808 : v8 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic , Differentiable dynamical systems |
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Call number: | SPRINGER-2013-9783642387425:ONLINE Show nearby items on shelf |
Title: | Monomial Ideals, Computations and Applications [electronic resource] |
Author(s): |
Anna M Bigatti Philippe Gimenez Eduardo Senz-de-Cabezn |
Date: | 2013 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This work covers three important aspects of monomials ideals in the three chapters Stanley decompositions by Jrgen Herzog, Edge ideals by Adam Van Tuyl and Local cohomology by Josep lvarez Montaner. The chapters,written by top experts, include comput er tutorials that emphasize the computational aspects of the respective areas. Monomial ideals and algebras are, in a sense, among the simplest structures in commutative algebra and the mainobjects of combinatorial commutative algebra. Also, they are of m ajor importance for at least three reasons. Firstly, Grbner basis theory allows us to treat certain problems on general polynomial ideals by means of monomial ideals.Secondly, the combinatorial structure of monomial ideals connects them to other combinato rial structures and allows us to solve problems on both sides of this correspondence using the techniques of each of the respective areas. Andthirdly, the combinatorial nature of monomial ideals also makes them particularly well suited to the development of algorithms to work with them and then generate algorithms for more general structures |
Note: | Springer eBooks |
Contents: | A survey on Stanley depth |
Stanley decompositions using CoCoA | |
A beginners guide to edge and cover ideals | |
Edge ideals using Macaulay2 | |
Local cohomology modules supported on monomial ideals | |
Local Cohomology using Macaulay2 | |
ISBN: | 9783642387425 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2083 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2013-9781461469988:ONLINE Show nearby items on shelf |
Title: | Algebraic Combinatorics [electronic resource] : Walks, Trees, Tableaux, and More |
Author(s): |
Richard P Stanley |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the authors extensiveknowledge of combinatori cs and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfoundknowledge to mathematical, engineering, and bus iness models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory.Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints toselected exercises. Key topics include walks on graphs, cubes and the Radon transform, the MatrixTree Th eorem, de Bruijn sequences, the Erds-Moser conjecture, electrical networks, and the Sperner property. There are also threeappendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and t he enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics atthe Massachusetts Institute of Technology. Stanley has received several awards including the George Plya Prize in applied combinatorics, the Guggenheim Fello wship, and the Leroy P. Steele Prize for mathematical exposition. Also bythe author: Combinatorics and Commutative Algebra, Second Edition, Birkhuser |
Note: | Springer eBooks |
Contents: | Preface |
Notation | |
1. Walks in graphs | |
2. Cubes and the Radon transform | |
3. Random walks | |
4. The Sperner property | |
5. Group actions on boolean algebras | |
6. Young diagrams and q | |
binomial coefficients | |
7. Enumeration under group action | |
8. A glimpse of Young tableaux | |
Appendix. The RSK algorithm | |
Appendix. Plane partitions | |
9. The MatrixTree Theorem | |
Appendix. Three elegant combinatorial proofs | |
10. Eulerian diagraphs and oriented trees | |
11. Cycles, bonds, and electrical networks | |
12. Miscellaneous gems of algebraic combinatorics | |
Hints | |
References | |
ISBN: | 9781461469988 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Undergraduate Texts in Mathematics, 0172-6056 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Combinatorics |
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Call number: | SPRINGER-2013-9781461459873:ONLINE Show nearby items on shelf |
Title: | Introduction to Commutative Algebra and Algebraic Geometry [electronic resource] |
Author(s): |
Ernst Kunz |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Originally published in 1985, this classic textbook is an English translation of Einfhrung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhuser Classics series, the publisher is proud to makeIntroduction to Commutati ve Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representationof algebraic varieties as intersections of the least possible number of hypersurfaces anda closely related problemwith the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basicconcepts of commutative algebra and algebraic geometry and proves many facts whic h can then serve as a basic stock for a deeper study of these subjects |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Preface to the English Edition | |
Terminology | |
Algebraic varieties | |
Dimension | |
Regular and rational functions on algebraic varieties | |
The local | |
global principle in commutative algebra | |
On the number of equations needed to describe an algebraic variety | |
Regular and singular points of algebraic varieties | |
Projective Resolutions | |
Bibliography | |
List of Symbols | |
Index. | |
ISBN: | 9781461459873 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Modern Birkhuser Classics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic |
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Call number: | SPRINGER-2013-9781461454502:ONLINE Show nearby items on shelf |
Title: | Lectures on Finitely Generated Solvable Groups [electronic resource] |
Author(s): |
Katalin A Bencsath Marianna C Bonanome Margaret H Dean Marcos Zyman |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Lectures on Finitely Generated Solvable Groups are based on the Topics in Group Theory course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Centerof the City University of Ne w York. While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them. The study of finitely generatedsolvable groups involves many different threads thereforethe se notes contain discussions on HNN extensions amalgamated and wreath products and other concepts from combinatorial group theory as well as commutative algebra. Alongwith Baumslags Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvablegroups. Examples are also supplied, which help illuminate many of the key concepts contained in the notes. Requiring onl y a modest initial group theory background from graduate and post-graduate students, these notes provide afield guide to the class of finitely generated solvable groups froma combinatorial group theory perspective |
Note: | Springer eBooks |
Contents: | Foreword |
Preface | |
Preliminaries | |
Tools: Presentations and their Calculus | |
Constructions | |
Representations andaTheorem of Krasner and Kaloujnine | |
The Bieri | |
Strebel Theorems | |
Finitely Generated Metabelian Groups | |
An Embedding Theorem for Finitely Generated Metabelian Groups | |
Sketch of Proof of Lemma 1.1 | |
Theorem 2.1 Details | |
Presenting an (Internal) HNN | |
Extension | |
References | |
ISBN: | 9781461454502 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | SpringerBriefs in Mathematics, 2191-8198 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Combinatorics |
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Call number: | SPRINGER-2013-9781461452928:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday |
Author(s): |
Irena Peeva |
Date: | 2013 |
Publisher: | New York, NY : Springer New York : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This contributed volume brings together the highest quality expository papers written by leaders and talented junior mathematicians in the field of Commutative Algebra. Contributions cover a very wide range of topics, includingcore areas in Commutati ve Algebra and also relations to Algebraic Geometry, Algebraic Combinatorics, Hyperplane Arrangements, Homological Algebra, and String Theory. The book aims to showcase the area, especially for the benefit ofjunior mathematicians and researchers who are n ew to the field it will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many openproblems are discussed with the aspiration to inspire the readers and foster further research |
Note: | Springer eBooks |
Contents: | Marian Aprodu: Lazarfeld |
Mukai bundles and applications to syzygies | |
Paul Aspinwall: Some Applications of Commutative Algebra to String Theory | |
Angelica Benito, Eleonore Faber, and Karen Smith: Measuring singularities with Frobenius: the basics | |
Christine Berkesch, Daniel Erman, and Manoj Kumini: Three avors of extremal Betti tables | |
Manuel Blickle and Karl Schwede: p1 linear maps in algebra and geometry | |
Markus Brodmann, Cao Luy Linh, and Maria | |
Helena Seiler: Castelnuovo | |
Mumford Regularity of Annihilators, Ext | |
Modules and Tor | |
Modules | |
David Buchsbaum: Selections From the Letter | |
Pl | |
ISBN: | 9781461452928 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2013-9781447148296:ONLINE Show nearby items on shelf |
Title: | Algebraic Geometry and Commutative Algebra [electronic resource] |
Author(s): |
Siegfried Bosch |
Date: | 2013 |
Publisher: | London : Springer London : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover,Grothendiecks schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved theway to spectacular progress such as the proof of Fermats Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broadentheir view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter ofthe book is preceded by a motivating introduction with an informal discussion of the contents. Typical exa mples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourselfor for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature |
Note: | Springer eBooks |
Contents: | Rings and Modules |
The Theory of Noetherian Rings | |
Integral Extensions | |
Extension of Coefficients and Descent | |
Homological Methods: Ext and Tor | |
Affine Schemes and Basic Constructions | |
Techniques of Global Schemes | |
Etale and Smooth Morphisms | |
Projective Schemes and Proper Morphisms | |
ISBN: | 9781447148296 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext, 0172-5939 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2012-9783642303623:ONLINE Show nearby items on shelf |
Title: | Algebraic Operads [electronic resource] |
Author(s): |
Jean-Louis Loday Bruno Vallette |
Date: | 2012 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In many areas of mathematics some higher operations are arising. These have become so important that several research projects refer to such expressions. Higher operations form new types of algebras. The key tounderstanding and comparing them, to cre ating invariants of their action is operad theory. This is a point of view that is 40 years old in algebraic topology, but the new trend is its appearance in several other areas, such asalgebraic geometry, mathematical physics, differential geometry, and combinatorics. The present volume is the first comprehensive and systematic approach to algebraic operads. An operad is an algebraic device that serves to study allkinds of algebras (associative, commutative, Lie, Poisson, A-infinity, etc.) from a concept ual point of view. The book presents this topic with an emphasis on Koszul duality theory. After a modern treatment of Koszul duality forassociative algebras, the theory is extended to operads. Applications to homotopy algebra are given, for instance the HomotopyTransfer Theorem. Although the necessary notions of algebra are recalled, readers areexpected to be familiarwith elementary homological algebra. Each chapter ends with a helpful summary and exercises. A full chapter is devoted to examples, and num erous figures are included. After an elementary chapter on classical algebra, accessible toundergraduate students,the level increases gradually through the book. However, the authors have done their best to make it suitable for graduate students: three ap pendices review the basic results needed in order to understand thevarious chapters. Since higher algebra is becoming essential in several research areas like deformation theory, algebraic geometry, representation theory, differential geometry, algebraic combinatorics, and mathematical physics, thebook can also be used as a reference work by researchers. |
Note: | Springer eBooks |
Contents: | Preface |
1.Algebras, coalgebras, homology | |
2.Twisting morphisms | |
3.Koszul duality for associative algebras | |
4.Methods to prove Koszulity of an algebra | |
5.Algebraic operad | |
6 Operadic homological algebra | |
7.Koszul duality of operads | |
8.Methods to prove Koszulity of an operad | |
9.The operads As and A\infty | |
10.Homotopy operadic algebras | |
11.Bar and cobar construction of an algebra over an operad | |
12.(Co)homology of algebras over an operad | |
13.Examples of algebraic operads | |
Apendices: A.The symmetric group | |
B.Categories | |
C.Trees | |
References | |
Index | |
List of Not | |
ISBN: | 9783642303623 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v346 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology , Cell aggregation Mathematics |
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Call number: | SPRINGER-2012-9783034804110:ONLINE Show nearby items on shelf |
Title: | Mathematical Methods in Systems, Optimization, and Control [electronic resource] : Festschrift in Honor of J. William Helton |
Author(s): |
Harry Dym Mauricio C Oliveira Mihai Putinar |
Date: | 2012 |
Publisher: | Basel : Springer Basel : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume is dedicated to Bill Helton on the occasion of his sixty-fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization andcontrol, and 19 techn ical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty-oddyears. These include interpolation, Szeg limi t theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful tograduate students in mathematics and engineering, as well as to facult y and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure andapplied mathematicsand engineering, and as a source book for seminars |
Note: | Springer eBooks |
Contents: | Preface |
Inroduction (an overview of the contents of the book, from the perspective of Helton's landmark contributions) | |
Biographical Note and List of Publications of J.W. Helton | |
Bounded Analytic Interpolation and H | |
infinity Control | |
Linear Matrix Inequalities and Matrix Convexity | |
Optimization and Realization in the Free * | |
algebra | |
Automatic Verification of Matrix Inequalities | |
Non | |
commutative Algebraic Geometry | |
Non | |
Commutative Differential Geometry and Probability | |
Modern Trends in Robust Control | |
Challenges of Mathematical Biology | |
Mathematical Programming and Comput | |
ISBN: | 9783034804110 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v222 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Functions of complex variables , Operator theory |
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Call number: | SPRINGER-2012-9783034802604:ONLINE Show nearby items on shelf |
Title: | Representations of Finite Groups: Local Cohomology and Support [electronic resource] |
Author(s): |
David J Benson Srikanth Iyengar Henning Krause |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas fromcommutative algebra, co homology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been DanielQuillens description of the algebraic variety co rresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods ofalgebraic geometry to obtain representation theoretic information. Thei r work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutativeHopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins classification ofthick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localiz ing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approachto address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with rin g of operators. The book serves as an introduction to this circle of ideas |
Note: | Springer eBooks |
Contents: | Preface |
1 Monday | |
1.1 Overview | |
1.2 Modules over group algebras | |
1.3 Triangulated categories | |
1.4 Exercises | |
2 Tuesday | |
2.1 Perfect complexes over commutative rings | |
2.2 Brown representability and localization | |
2.3 The stable module category of a finite group | |
2.4 Exercises | |
3 Wednesday | |
3.1 | |
3.2 Koszul objects and support | |
3.3 The homotopy category of injectives | |
3.4 Exercises | |
4 Thursday | |
4.1 Stratifying triangulated categories | |
4.2 Consequences of stratification | |
4.3 The Klein four group | |
4.4 Exercises | |
5 Friday | |
5.1 Localising subcategories of D | |
ISBN: | 9783034802604 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Oberwolfach Seminars : v43 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2012-9783034802215:ONLINE Show nearby items on shelf |
Title: | A Panorama of Modern Operator Theory and Related Topics [electronic resource] The Israel Gohberg Memorial Volume |
Author(s): |
Harry Dym Marinus A Kaashoek Peter Lancaster Heinz Langer Leonid Lerer |
Date: | 2012 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is dedicated to the memory of Israel Gohberg (19282009) one of the great mathematicians of our time who inspired innumerable fellow mathematicians and directed many students. The volume reflects the widespectrum of Gohbergs mathematical i nterests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single andmultivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structuredmatrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory |
Note: | Springer eBooks |
ISBN: | 9783034802215 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v218 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Matrix theory , Functional analysis , Operator theory , Differential equations, partial , Systems theory |
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Call number: | SPRINGER-2012-9781447127307:ONLINE Show nearby items on shelf |
Title: | Finitely Generated Abelian Groups and Similarity of Matrices over a Field [electronic resource] |
Author(s): |
Christopher Norman |
Date: | 2012 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version ofthe Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part1 of this book provides a measured introduction to such groups: two finitely generated abelian groups areisomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part2 starting with matrices having polynomial entries: two matrices over a fieldare similar if and only if their rational canonical forms are equal. Unde r certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with theelementary properties of rings and fields. Also a knowledge of abstract linear algebra including vect or spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but froma more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerousworked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates . The later chapters, which cover closely related topics, e.g. field extensions,endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra |
Note: | Springer eBooks |
Contents: | Part 1 :Finitely Generated Abelian Groups: Matrices with Integer Entries: The Smith Normal Form |
Basic Theory of Additive Abelian Groups | |
Decomposition of Finitely Generated Z | |
Modules. Part 2: Similarity of Square Matrices over a Field: The Polynomial Ring F[x]and Matrices over F[x] | |
F[x] Modules: Similarity of t xtMatrices over a Field F | |
Canonical Forms and Similarity Classes of Square Matrices over a Field. | |
ISBN: | 9781447127307 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Undergraduate Mathematics Series, 1615-2085 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Field theory (Physics) , Group theory , Matrix theory , Algorithms |
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Call number: | SPRINGER-2012-9780817646424:ONLINE Show nearby items on shelf |
Title: | Sheaves of Algebras over Boolean Spaces [electronic resource] |
Author(s): |
Arthur Knoebel |
Date: | 2012 |
Publisher: | Boston, MA : Birkhuser Boston : Imprint: Birkhuser |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Sheaves of Algebras over Boolean Spaces comprehensively covers sheaf theory as applied to universal algebra. Sheaves decompose general algebras into simpler pieces called the stalks. A classical case is commutative von Neumannregular rings, whose sta lks are fields. Other classical theorems also extend to shells, a common generalization of rings and lattices. This text presents intuitive ideas from topology such as the notion of metric space and the conceptof central idempotent from ring theory. These lead to the abstract notions of complex and factor element, respectively. Factor elements are defined by identities, discovered for shells for the first time, explaining why centralelements in rings and lattices have their particular form. Categorical fo rmulations of the many representations by sheaves begin with adjunctions and move to equivalences as the book progresses, generalizing Stones theorem forBoolean algebras. Half of the theorems provided in the text are new the rest are presented in a cohere nt framework, starting with the most general, and proceeding to specific applications. Many open problems and research areas areoutlined, including a final chapter summarizing applications of sheaves in diverse fields that were not covered earlier in the book. This monograph is suitable for graduate students and researchers, and it will serve as an excellentreference text for those who wish to learn about sheaves of algebras |
Note: | Springer eBooks |
Contents: | Preface |
Introduction | |
Algebra | |
Tools | |
Complexes and their Sheaves | |
Boolean Subsemilattices | |
Sheaves from Factor Congruences | |
Shells | |
Baer | |
Stone Shells | |
Strict Shells | |
Varieties Generated by Preprimal Algebras | |
Return to General Algebras | |
Further Examples Pointing to Future Research | |
List of Symbols | |
References | |
Index | |
ISBN: | 9780817646424 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Topology |
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Call number: | SPRINGER-2011-9783834881595:ONLINE Show nearby items on shelf |
Title: | Lectures on Algebraic Geometry II [electronic resource] : Basic Concepts, Coherent Cohomology, Curves and their Jacobians |
Author(s): |
Gnter Harder |
Date: | 2011 |
Publisher: | Wiesbaden : Vieweg+Teubner |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In this second volume of Lectures on Algebraic Geometry, the author starts with some foundational concepts in the theory of schemes and gives a somewhat casual introduction into commutative algebra. After that he proves thefiniteness results for cohe rent cohomology and discusses important applications of these finiteness results. In the two last chapters, curves and their Jacobians are treated and some outlook into further directions of research isgiven. The first volume is not necessarily a prerequi site for the second volume if the reader accepts the concepts on sheaf cohomology. On the other hand, the concepts and results in the second volume have been historically inspired bythe theory of Riemann surfaces. There is a deep connection between these two volumes, in spirit they form a unity. Basic concepts of the Theory of Schemes - Some Commutative Algebra - Projective Schemes - Curves and the Theorem ofRiemann-Roch - The Picard functor for curves and Jacobians. Prof. Dr. Gnter Harder, Department of Mathematics, University of Bonn, and Max-Planck-Institute for Mathematics, Bonn, Germany |
Note: | Springer eBooks |
ISBN: | 9783834881595 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry |
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Call number: | SPRINGER-2011-9783642204388:ONLINE Show nearby items on shelf |
Title: | Classical Summation in Commutative and Noncommutative L_{p}-Spaces [electronic resource] |
Author(s): |
Andreas Defant |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series innoncommutative $L_p$-spaces co nstructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space together with a faithful normal state on this algebra) |
Note: | Springer eBooks |
Contents: | 1 Introduction |
2 Commutative Theory | |
3 Noncommutative Theory | |
ISBN: | 9783642204388 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v2021 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Global analysis (Mathematics) , Fourier analysis , Functional analysis , Distribution (Probability theory) |
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Call number: | SPRINGER-2011-9783642194924:ONLINE Show nearby items on shelf |
Title: | Combinatorial Aspects of Commutative Algebra and Algebraic Geometry [electronic resource] : The Abel Symposium 2009 |
Author(s): |
Gunnar Flystad Trygve Johnsen Andreas Leopold Knutsen |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The Abel Symposium 2009 Combinatorial aspects of Commutative Algebra and Algebraic Geometry, held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presentingcontributions on syzygies, trop ical geometry, Boij-Sderberg theory, Schubert calculus, and quiver varieties. The volume also includes an introductory survey on binomial ideals with applications to hypergeometric series, combinatorialgames and chemical reactions. The contributions pose interesting problems, and offer up-to-date research on some of the most active fields of commutative algebra and algebraic geometry with a combinatorial flavour |
Note: | Springer eBooks |
Contents: | The Cone of Betti Diagrams of Bigraded Artinian Modules of Codimension Two: M.Boij, G.Flystad |
Koszul Cycles: W.Bruns, A.Conca, T.Rmer | |
Boij | |
Sderberg Theory: D.Eisenbud, F | |
O.Schreyer | |
Powers of Componentwise Linear Ideals: J.Herzog, T.Hibi, H.Ohsugi | |
Modules With 1 | |
Dimensional Socle and Components of Lusztig Quiver Varieties in Type A.: J.Kamnitzer, C.Sadanand | |
Realization Spaces for Tropical Fans: E.Katz, S.Payne | |
A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus: D.Laksov | |
Theory and Applications of Lattice Po | |
ISBN: | 9783642194924 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Abel Symposia : v6 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Combinatorics |
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Call number: | SPRINGER-2011-9783642174049:ONLINE Show nearby items on shelf |
Title: | Modular Invariant Theory [electronic resource] |
Author(s): |
H.E.A. Eddy Campbell David L Wehlau |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group. It explains a theory that is more complicated than the study of the classicalnon-modular case, and it descri bes many open questions. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the betterunderstood non-modular setting. It details techniques f or the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of manytopics as well as a quick survey of the elements of algebraic geometry and com mutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchersan introduction to many important topics inmodern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter |
Note: | Springer eBooks |
Contents: | 1 First Steps |
2 Elements of Algebraic Geometry and Commutative Algebra | |
3 Applications of Commutative Algebra to Invariant Theory | |
4 Examples | |
5 Monomial Orderings and SAGBI Bases | |
6 Block Bases | |
7 The Cyclic Group Cp | |
8 Polynomial Invariant Rings | |
9 The Transfer | |
10 Invariant Rings via Localization | |
11 Rings of Invariants which are Hypersurfaces | |
12 Separating Invariants | |
13 Using SAGBI Bases to Compute Rings of Invariants | |
14 Ladders | |
References | |
Index | |
ISBN: | 9783642174049 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Encyclopaedia of Mathematical Sciences, 0938-0396 : v139 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic |
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Call number: | SPRINGER-2011-9783642110368:ONLINE Show nearby items on shelf |
Title: | Some Aspects of Ring Theory [electronic resource] |
Author(s): |
I. N Herstein |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | S. Amitsur: Associative rings with identities.- I.N. Herstein: Topics in ring theory.- N. Jacobson: Representation theory of Jordan algebras.- I. Kaplansky: The theory of homological dimension.- D. Buchsbaum: Complexes in localring theory.- P.H. Cohn : Two topics in ring theory.- A.W. Goldie: Non-commutative localisation |
Note: | Springer eBooks |
Contents: | S. Amitsur: Associative rings with identities |
I.N. Herstein: Topics in ring theory | |
N. Jacobson: Representation theory of Jordan algebras | |
I. Kaplansky: The theory of homological dimension | |
D. Buchsbaum: Complexes in local ring theory | |
P.H. Cohn: Two topics in ring theory | |
A.W. Goldie: Non | |
commutative localisation | |
ISBN: | 9783642110368 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v37 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Differential equations, partial |
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Call number: | SPRINGER-2011-9783642109799:ONLINE Show nearby items on shelf |
Title: | Categories and Commutative Algebra [electronic resource] |
Author(s): |
P Salmon |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | L. Badescu: Sur certaines singularits des varits algbriques.- D.A. Buchsbaum: Homological and commutative algebra.- S. Greco: Anelli Henseliani.- C. Lair: Morphismes et structures algbriques.- B.A. Mitchell:Introduction to category theory and homolog ical algebra.- R. Rivet: Anneaux de sries formelles et anneaux henseliens.- P. Salmon: Applicazioni della K-teoria allalgebra commutativa.- M. Tierney: Axiomatic sheaf theory: someconstructions and applications.- C.B. Winters: An elementary lecture on alg ebraic spaces |
Note: | Springer eBooks |
Contents: | L. Badescu: Sur certaines singularits des varits algbriques |
D.A. Buchsbaum: Homological and commutative algebra | |
S. Greco: Anelli Henseliani | |
C. Lair: Morphismes et structures algbriques | |
B.A. Mitchell: Introduction to category theory and homological algebra | |
R. Rivet: Anneaux de sries formelles et anneaux henseliens | |
P. Salmon: Applicazioni della K | |
teoria allalgebra commutativa | |
M. Tierney: Axiomatic sheaf theory: some constructions and applications | |
C.B. Winters: An elementary lecture on algebraic spaces | |
ISBN: | 9783642109799 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | C.I.M.E. Summer Schools : v58 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2011-9783642035456:ONLINE Show nearby items on shelf |
Title: | A Course in Commutative Algebra [electronic resource] |
Author(s): |
Gregor Kemper |
Date: | 2011 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrateson the concepts and re sults at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, threechapters are devoted to computational aspects. M any illustrative examples and exercises enrich the text |
Note: | Springer eBooks |
Contents: | Introduction |
Part I The Algebra Geometry Lexicon: 1 Hilbert's Nullstellensatz 2 Noetherian and Artinian Rings 3 The Zariski Topology 4 A Summary of the Lexicon | |
Part II Dimension: 5 Krull Dimension and Transcendence Degree 6 Localization 7 The Principal Ideal Theorem 8 Integral Extensions | |
Part III Computational Methods: 9 Grbner Bases 10 Fibers and Images of Morphisms Revisited 11 Hilbert Series and Dimension | |
Part IV Local Rings: 12 Dimension Theory 13 Regular Local Rings 14 Rings of Dimension One | |
References | |
Notation | |
Index | |
ISBN: | 9783642035456 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v256 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra , Computer science Mathematics |
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Call number: | SPRINGER-2011-9781441969903:ONLINE Show nearby items on shelf |
Title: | Commutative Algebra [electronic resource] : Noetherian and Non-Noetherian Perspectives |
Author(s): |
Marco Fontana Salah-Eddine Kabbaj Bruce Olberding Irena Swanson |
Date: | 2011 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutativealgebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters are internationally renowned for their important contributions to various aspects ofcurrent research in commutative algebra. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions,tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying commutative algebra |
Note: | Springer eBooks |
Contents: | Introduction |
1. Principal | |
like Ideals and Related Polynomial Content Conditions (D.D. Anderson) | |
2. Zero | |
divisor Graphs in Commutative Rings (D.F. Anderson, M. Axtell, J. Stickles) | |
3. Class Semigroups and T | |
class Semigroups of Domains (S. Bazzoni, S. Kabbaj) | |
4. Forcing Algebras, Syzygy Bundles, and Tight Closure (H. Brenner) | |
5. Beyond Totally Reflexive Modules and Back: A Survey on Gorenstein Dimensions (L.W. Christensen, H.B. Foxby, H. Holm) | |
6. On V | |
domains: A Survey (M. Fontana, M. Zafrullah) | |
7. Tensor Products of Algebras Over a Field (H. Haghighi, M. Tousi, S. Yassemi | |
ISBN: | 9781441969903 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2011-9780857291837:ONLINE Show nearby items on shelf |
Title: | Non-commutative Gelfand Theories [electronic resource] : A Tool-kit for Operator Theorists and Numerical Analysts |
Author(s): |
Steffen Roch Pedro A Santos Bernd Silbermann |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Written as a hybrid between a research monograph and a textbook the first half of this book is concerned with basic concepts for the study of Banach algebras that, in a sense, are not too far from being commutative. Essentially,the algebra under cons ideration either has a sufficiently large center or is subject to a higher order commutator property (an algebra with a so-called polynomial identity or in short: Pl-algebra). In the second half of the book, anumber of selected examples are used to demons trate how this theory can be successfully applied to problems in operator theory and numerical analysis. Distinguished by the consequent use of local principles (non-commutative Gelfandtheories), PI-algebras, Mellin techniques and limit operator technique s, each one of the applications presented in chapters 4, 5 and 6 forms a theory that is up to modern standards and interesting in its own right. Written in a waythat can be worked through by the reader with fundamental knowledge of analysis, functional an alysis and algebra, this book will be accessible to 4th year students of mathematics or physics whilst also being of interest to researchersin the areas of operator theory, numerical analysis, and the general theory of Banach algebras |
Note: | Springer eBooks |
Contents: | Banach algebras |
Local principles | |
Banach algebras generated by idempotents | |
Singular integral operators | |
Convolution operators | |
Algebras of operator sequences | |
ISBN: | 9780857291837 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Universitext |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Fourier analysis , Functional analysis , Integral equations , Operator theory , Numerical analysis |
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Call number: | SPRINGER-2011-9780857291776:ONLINE Show nearby items on shelf |
Title: | Graded Syzygies [electronic resource] |
Author(s): |
Irena Peeva |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The study of free resolutions is a core and beautiful area in Commutative Algebra. The main goal of this book is to inspire the readers and develop their intuition about syzygies and Hilbert functions. Many examples are given inorder to illustrate id eas and key concepts. A valuable feature of the book is the inclusion of open problems and conjectures these provide a glimpse of exciting, and often challenging, research directions in the field. Three types ofproblems are presented: Conjectures, Problem s, and Open-Ended Problems. The latter do not describe specific problems but point to interesting directions for exploration. The first part of the monograph contains basic backgroundmaterial on graded free resolutions. Further coverage of topics includes syzygies over a polynomial ring, resolutions over quotient rings, lex ideals and Hilbert functions, compression, resolutions of monomial ideals, and syzygies oftoric ideals. With a clear and self-contained exposition this text is intended for advanced gr aduate students and postdoctorates it will be also of interest to senior mathematicians |
Note: | Springer eBooks |
Contents: | Graded Free Resolutions |
Hilbert Functions | |
Monomial Resolutions | |
Syzygies of Toric Ideals | |
ISBN: | 9780857291776 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications : v14 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2011-9780857291066:ONLINE Show nearby items on shelf |
Title: | Monomial Ideals [electronic resource] |
Author(s): |
Jrgen Herzog Takayuki Hibi |
Date: | 2011 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book demonstrates current trends in research on combinatorial and computational commutative algebra with a primary emphasis on topics related to monomial ideals. Providing a useful and quick introduction to areas of researchspanning these fields , Monomial Ideals is split into three parts. Part I offers a quick introduction to the modern theory of Grbner bases as well as the detailed study of generic initial ideals. Part II supplies Hilbert functions andresolutions and some of the combinatorics r elated to monomial ideals including the KruskalKatona theorem and algebraic aspects of Alexander duality. Part III discusses combinatorial applications of monomial ideals, providing avaluable overview of some of the central trends in algebraic combinatori cs. Main subjects include edge ideals of finite graphs, powers of ideals, algebraic shifting theory and an introduction to discrete polymatroids. Theory iscomplemented by a number of examples and exercises throughout, bringing the reader to a deeper under standing of concepts explored within the text. Self-contained and concise, this book will appeal to a wide range of readers, includingPhD students on advanced courses, experienced researchers, and combinatorialists and non-specialists with a basic knowled ge of commutative algebra. Since their first meeting in 1985, Juergen Herzog (Universitt Duisburg-Essen,Germany) and Takayuki Hibi (Osaka University, Japan), have worked together on a number of research projects, of which recent results are presented in t his monograph |
Note: | Springer eBooks |
Contents: | Part I Grbner bases: Monomial Ideals |
A short introduction to Grbner bases | |
Monomial orders and weights | |
Generic initial ideals | |
The exterior algebra | |
Part II: Hilbert functions and resolutions | |
Hilbert functions and the theorems of Macaulay and Kruskal | |
Katona | |
Resolutions of monomial ideals and the Eliahou | |
Kervaire formula | |
Alexander duality and resolutions | |
Part III Combinatorics: Alexander duality and finite graphs | |
Powers of monomial ideals | |
Shifting theory | |
Discrete Polymatroids | |
Some homological algebra | |
Geometry | |
ISBN: | 9780857291066 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v260 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2010-9783834897220:ONLINE Show nearby items on shelf |
Title: | Algebraic Geometry I [electronic resource] : Schemes With Examples and Exercises |
Author(s): |
Ulrich Grtz Torsten Wedhorn |
Date: | 2010 |
Publisher: | Wiesbaden : Vieweg+Teubner |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. Asystematic treatment an d motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically todiscuss the covered techniques. Thus the rea der experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check thecomprehension of the text, treat further examples, or give an ou tlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essentialfacts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local propertiesof schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes -Examples Prof. Dr. Ulrich Grtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Dep artment of Mathematics, University of Paderborn |
Note: | Springer eBooks |
ISBN: | 9783834897220 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2010-9783642142406:ONLINE Show nearby items on shelf |
Title: | Hilbert Functions of Filtered Modules [electronic resource] |
Author(s): |
Giuseppe Valla Maria Evelina Rossi |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Hilbert functions play major parts in Algebraic Geometry and Commutative Algebra, and are also becoming increasingly important in Computational Algebra. They capture many useful numerical characters associated to a projectivevariety or to a filtered module over a local ring. Starting from the pioneering work of D.G. Northcott and J. Sally, we aim to gather together in one book a broad range of new developments in this theory by using a unifying approachwhich yields self-contained and easier proofs. T he extension of the theory to the case of general filtrations on a module, and its application to the study of certain graded algebras which are not associated to a filtration are two ofthe main features of this work. The material is intended for graduate students and researchers who are interested in Commutative Algebra, particularly in the theory of the Hilbert functions and related topics |
Note: | Springer eBooks |
ISBN: | 9783642142406 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes of the Unione Matematica Italiana, 1862-9113 : v9 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Geometry, algebraic |
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Call number: | SPRINGER-2010-9783642133688:ONLINE Show nearby items on shelf |
Title: | The Use of Ultraproducts in Commutative Algebra [electronic resource] |
Author(s): |
Hans Schoutens |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | In spite of some recent applications of ultraproducts in algebra, they remain largely unknown to commutative algebraists, in part because they do not preserve basic properties such as Noetherianity. This work wants to make astrong case against these prejudices. More precisely, it studies ultraproducts of Noetherian local rings from a purely algebraic perspective, as well as how they can be used to transfer results between the positive and zerocharacteristics, to derive uniform bounds, to define tight closure in characteristic zero, and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants calledchromatic products, which are often even Noetherian. This book, neither assuming nor using any logical formalism, is intended for algebraists and geometers, in the hope of popularizing ultraproducts and their applications in algebra |
Note: | Springer eBooks |
Contents: | Ultraproducts and ?o? Theorem |
Flatness | |
Uniform Bounds | |
Tight Closure in Positive Characteristic | |
Tight Closure in Characteristic Zero. Affine Case | |
Tight Closure in Characteristic Zero. Local Case | |
Cataproducts | |
Protoproducts | |
Asymptotic Homological Conjectures in Mixed Characteristic | |
ISBN: | 9783642133688 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1999 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Geometry, algebraic , Algebra |
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Call number: | SPRINGER-2010-9783642111754:ONLINE Show nearby items on shelf |
Title: | Introduction to Complex Reflection Groups and Their Braid Groups [electronic resource] |
Author(s): |
Michel Brou |
Date: | 2010 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Weyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently beendiscovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductivegroups. It is now also broadly agreed upon that ma ny of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic propertiesof complex reflection groups (characterization, Steinberg theorem, Gutki n-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basicdefinitions and properties of the associated braid groups, as well as a quick introduction to Bes sis' lifting of Springer theory to braid groups |
Note: | Springer eBooks |
Contents: | 1 Preliminaries |
2 Prerequsites and Complements in Commutative Algebra | |
3 Polynomial Invariants of Finite Linear Groups | |
4 Finite Reflection Groups in Characteristic Zero | |
5 Eigenspaces and Regular Elements | |
ISBN: | 9783642111754 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1988 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Algebraic topology |
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Call number: | SPRINGER-2010-9783211993149:ONLINE Show nearby items on shelf |
Title: | Approximate Commutative Algebra [electronic resource] |
Author(s): |
Lorenzo Robbiano John Abbott |
Date: | 2010 |
Publisher: | Vienna : Springer Vienna |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | Approximate Commutative Algebra is an emerging field of research which endeavours to bridge the gap between traditional exact Computational Commutative Algebra and approximate numerical computation. The last 50 years have seenenormous progress in the realm of exact Computational Commutative Algebra, and given the importance of polynomials in scientific modelling, it is very natural to want to extend these ideas to handle approximate, empirical data derivingfrom physical measurements of phenomena in t he real world. In this volume nine contributions from established researchers describe various approaches to tackling a variety of problems arising in Approximate Commutative Algebra |
Note: | Springer eBooks |
Contents: | From Oil Fields to Hilbert Schemes |
Numerical Decomposition of the Rank | |
Deficiency Set of a Matrix of Multivariate Polynomials | |
Towards Geometric Completion of Differential Systems by Points | |
Geometric Involutive Bases and Applications to Approximate Commutative Algebra | |
Regularization and Matrix Computation in Numerical Polynomial Algebra | |
Ideal Interpolation: Translations to and from Algebraic Geometry | |
An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint | |
ApCoA = Embedding Commutative Algebra into Analysis | |
Exact Certification in Global Polynomia | |
ISBN: | 9783211993149 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Texts and Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 0943-853X |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra Data processing , Geometry, algebraic , Algebra , Numerical analysis |
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Call number: | SPRINGER-2010-9783034800525:ONLINE Show nearby items on shelf |
Title: | Simplicial Methods for Operads and Algebraic Geometry [electronic resource] |
Author(s): |
Ieke Moerdijk Bertrand Ton |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijks lectures offer a detailed introduction to dendroidal sets, which wereintroduced by himself and Weiss a s a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it alsoreveals new phenomena. For example, dendroidal sets ad mit a closed symmetric monoidal structure related to the BoardmanVogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with asuitable model structure on the category of dendroidal sets. Important concepts ar e illustrated with pictures and examples. The lecture series by Ton presents derived algebraic geometry. While classical algebraic geometry studiesfunctors from the category of commutative rings to the category of sets, derived algebraic geometry is conce rned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derivedquotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent conditi on. These lectures provide a concise and focused introduction to this vast subject, glossing over manyof the technicalities that make the subjects research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Tons lectures, some background in algebraicgeometry is also necessary |
Note: | Springer eBooks |
ISBN: | 9783034800525 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Advanced Courses in Mathematics - CRM Barcelona |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Algebraic topology |
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Call number: | SPRINGER-2010-9783034605489:ONLINE Show nearby items on shelf |
Title: | Recent Trends in Toeplitz and Pseudodifferential Operators [electronic resource] : The Nikolai Vasilevskii Anniversary Volume |
Author(s): |
Roland Duduchava Israel Gohberg Sergei M Grudsky Vladimir Rabinovich |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
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Note: | The aim of the book is to present new results in operator theory and its applications. In particular, the book is devoted to operators with automorphic symbols, applications of the methods of modern operator theory anddifferential geometry to some pr oblems of theory of elasticity, quantum mechanics, hyperbolic systems of partial differential equations with multiple characteristics, Laplace-Beltrami operators on manifolds with singular points.Moreover, the book comprises new results in the theory of W iener-Hopf operators with oscillating symbols, large hermitian Toeplitz band matrices, commutative algebras of Toeplitz operators, and discusses a number of other topics |
Note: | Springer eBooks |
Contents: | The Life and Work of Nikolai Vasilevski |
On the Structure of the Eigenvectors of Large Hermitian Toeplitz Band Matrices | |
Complete Quasi | |
wandering Sets and Kernels of Functional Operators | |
Lions Lemma, Korns Inequalities and the Lam Operator on Hypersurfaces | |
On the Bergman Theory for Solenoidal and Irrotational Vector Fields, I: General Theory | |
Weighted Estimates of Generalized Potentials in Variable Exponent Lebesgue Spaces on Homogeneous Spaces | |
Wiener | |
Hopf Operators with Oscillating Symbols on Weighted Lebesgue Spaces | |
On the Ill | |
posed Hyperbolic Systems with a Multipl | |
ISBN: | 9783034605489 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v210 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Operator theory |
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Call number: | SPRINGER-2010-9783034600071:ONLINE Show nearby items on shelf |
Title: | Ring and Module Theory [electronic resource] |
Author(s): |
Toma Albu Gary F Birkenmeier Ali Erdogan Adnan Tercan |
Date: | 2010 |
Publisher: | Basel : Springer Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This volume features a collection of 13 peer-reviewed contributions consisting of expository/survey articles and research papers by 24 authors. Many of theses contributions were presented at the International Conference on Ringand Module Theory held at Hacettepe University in Ankara, Turkey, from August 18 to 22, 2008. The selected contributions examine wide-ranging and cutting-edge developments in various areas of algebra including ring theory, moduletheory, Hopf algebras, and commutative algebra. T he survey articles are written by well-known experts in their respective areas and provide an overview which is useful for researchers in the area as well as those looking for new orrelated fields to investigate. The research papers give a taste of curren t research. The variety of topics will be of interest to both graduate students and researchers |
Note: | Springer eBooks |
Contents: | Preface |
Research Articles | |
Open Problems | |
ISBN: | 9783034600071 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Trends in Mathematics |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra |
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Call number: | SPRINGER-2009-9783764388584:ONLINE Show nearby items on shelf |
Title: | Selected Works of A.I. Shirshov [electronic resource] |
Author(s): |
Leonid Bokut Ivan Shestakov Victor Latyshev Efim Zelmanov |
Date: | 2009 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (19211981). He was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groupsand projective planes. His name is associated with notions and results on Grbner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshovs Height Theorem,Lyndon-Shirshov words, Hall-Shirshov bases, Shirshovs theorem on the Kurosh problem for alternative and Jordan algebras, and Shirshovs theorem on the speciality of Jordan algebras with two generators. Shirshovs ideas were usedby his student Efim Zelmanov for the solution of the Restricted Burnside Problem. Several famous algebraists provide in this book detailed comments on the impact of Shirshovs work on current algebra |
Note: | Springer eBooks |
Contents: | From the contents: Publications of A.I. Shirshov: Subalgebras of free Lie algebras |
On the representation of Lie rings in associative rings | |
Subalgebras of free commutative and free anticommutative algebras | |
On special J | |
rings | |
Some theorems on embedding of rings | |
On some nonassociative nil | |
rings and algebraic algebras | |
On rings with identical relations | |
On free Lie rings | |
On a problem of Levitzki | |
Some problems in the theory of rings that are nearly associative | |
Some algorithmic problems for e | |
algebras | |
Some algorithmic problems for Lie algebras | |
On a hypothesis in the | |
ISBN: | 9783764388584 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Contemporary Mathematicians |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Mathematics_$xHistory |
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Call number: | SPRINGER-2009-9783642030642:ONLINE Show nearby items on shelf |
Title: | Blocks and Families for Cyclotomic Hecke Algebras [electronic resource] |
Author(s): |
Maria Chlouveraki |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The definition of Rouquier for the families of characters introduced by Lusztig for Weyl groups in terms of blocks of the Hecke algebras has made possible the generalization of this notion to the case of complex reflection groups.The aim of this book is to study the blocks and to determine the families of characters for all cyclotomic Hecke algebras associated to complex reflection groups. This volume offers a thorough study of symmetric algebras, coveringtopics such as block theory, representation t heory and Clifford theory, and can also serve as an introduction to the Hecke algebras of complex reflection groups |
Note: | Springer eBooks |
Contents: | 1 On Commutative Algebra |
2 On Blocks | |
3 On Essential Algebras | |
4 On Hecke Algebras | |
5 On the Determination of the Rouquier Blocks | |
A Clifford Theory and Schur Elements for Generic Hecke Algebras | |
ISBN: | 9783642030642 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Mathematics, 0075-8434 : v1981 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Group theory |
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Call number: | SPRINGER-2009-9783540853329:ONLINE Show nearby items on shelf |
Title: | Generalized Lie Theory in Mathematics, Physics and Beyond [electronic resource] |
Author(s): |
Sergei Silvestrov Eugen Paal Viktor Abramov Alexander Stolin |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to theinterplay between severa l rapidly expanding research fields in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensionsof differential calculus and geometry, non-ass ociative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book will be a useful source ofinspiration for a broad spectrum of researchers and for research students , and includes contributions from several large research communities in modern mathematics and physics. This volume consists of 5 parts comprising 25 chapters,which were contributed by 32 researchers from 12 different countries. All contributions in the v olume have been refereed |
Note: | Springer eBooks |
Contents: | Non |
Associative and Non | |
Commutative Structures for Physics | |
Moufang Transformations and Noether Currents | |
Weakly Nonassociative Algebras, Riccati and KP Hierarchies | |
Applications of Transvectants | |
Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics | |
A Rewriting Approach to Graph Invariants | |
Non | |
Commutative Deformations, Quantization, Homological Methods, and Representations | |
Graded q | |
Differential Algebra Approach to q | |
Connection | |
On Generalized N | |
Complexes Coming from Twisted Derivations | |
Remarks on Quantizations, Words and R | |
Matrices | |
Conn | |
ISBN: | 9783540853329 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Topological Groups , Mathematical physics |
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Call number: | SPRINGER-2009-9783540680307:ONLINE Show nearby items on shelf |
Title: | Homological Mirror Symmetry [electronic resource] : New Developments and Perspectives |
Author(s): |
Karl-Georg Schlesinger Maximilian Kreuzer Anton Kapustin |
Date: | 2009 |
Publisher: | Berlin, Heidelberg : Springer Berlin Heidelberg |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Homological Mirror Symmetry, the study of dualities of certain quantum field theories in a mathematically rigorous form, has developed into a flourishing subject on its own over the past years. The present volume bridges a gap inthe literature by pro viding a set of lectures and reviews that both introduce and representatively review the state-of-the art in the field from different perspectives. With contributions by K. Fukaya, M. Herbst, K. Hori, M. Huang, A.Kapustin, L. Katzarkov, A. Klemm, M. Konts evich, D. Page, S. Quackenbush, E. Sharpe, P. Seidel, I. Smith and Y. Soibelman, this volume will be a reference on the topic for everyone starting to work or actively working on mathematicalaspects of quantum field theory |
Note: | Springer eBooks |
Contents: | The Symplectic Geometry of Cotangent Bundles from a Categorical Viewpoint |
B | |
Type D | |
Branes in Toric CalabiYau Varieties | |
Topological String Theory on Compact CalabiYau: Modularity and Boundary Conditions | |
Gauge Theory, Mirror Symmetry, and the Geometric Langlands Program | |
Homological Mirror Symmetry and Algebraic Cycles | |
Notes on A | |
Algebras, A | |
Categories and Non | |
Commutative Geometry | |
On Non | |
Commutative Analytic Spaces Over Non | |
Archimedean Fields | |
Derived Categories and Stacks in Physics | |
ISBN: | 9783540680307 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Lecture Notes in Physics, 0075-8450 : v757 |
Series: | Physics and Astronomy (Springer-11651) |
Keywords: | Algebra , Mathematical physics |
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Call number: | SPRINGER-2009-9781848829411:ONLINE Show nearby items on shelf |
Title: | Group and Ring Theoretic Properties of Polycyclic Groups [electronic resource] |
Author(s): |
B.A.F Wehrfritz |
Date: | 2009 |
Publisher: | London : Springer London |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on someaspects of topology, ge ometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focusesspecifically on the ring theoretic properties of po lycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students andresearchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thusthe book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developmentsin the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups |
Note: | Springer eBooks |
Contents: | Foreword |
Some basic group theory | |
Some ring theory | |
Soluble linear groups | |
Further group | |
theoretic properties of polycyclic groups | |
Groups acting on finitely generated commutative rings | |
Prime ideals in polycyclic | |
group rings | |
The structure of modules over polycyclic groups | |
Semilinear and skew linear groups | |
ISBN: | 9781848829411 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Algebra and Applications : v10 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory |
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Call number: | SPRINGER-2009-9781441901606:ONLINE Show nearby items on shelf |
Title: | Numerical Semigroups [electronic resource] |
Author(s): |
J.C Rosales P. A Garca-Snchez |
Date: | 2009 |
Edition: | First |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from this broad exposition of thetopic. Key features of Num erical Semigroups include: - Content ranging from the basics to open research problems and the latest advances in the field - Exercises at the end of each chapter that expand upon and support thematerial - Emphasis on the computational aspects of the theo ry algorithms are presented to provide effective calculations - Many examples that illustrate the concepts and algorithms - Presentation of various connections betweennumerical semigroups and number theory, coding theory, algebraic geometry, linear progra mming, and commutative algebra would be of significant interest to researchers. Numerical Semigroups is accessible to first year graduatestudents, with only a basic knowledge of algebra required, giving the full background needed for readers not familiar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in otherfields such as algebraic geometry, number theory, and linear programming |
Note: | Springer eBooks |
Contents: | Introduction |
1. Notable Elements | |
2. Numerical Semigroups with Maximal Embedding Dimension | |
3. Irreducible Numerical Semigropus | |
4. Proportionally Modular Numerical Semigroups | |
5. The Quotient of a Numerical Semigroup by a Positive Integer | |
6. Families of Numerical Semigroups Closed Under Finite Intersections and Adjoin of the Frobenius Number | |
7. Presentations of a Numerical Semigroup | |
8. The Gluing of Numerical Semigroups | |
9. Numerical Semigroups with Embedding Dimension Three | |
10. The Structure of a Numerical Semigroup | |
Bibliography. List of Symbols. Index | |
ISBN: | 9781441901606 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt, 1389-2177 : v20 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , Group theory , Number theory |
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Call number: | SPRINGER-2009-9780387763569:ONLINE Show nearby items on shelf |
Title: | Polytopes, Rings, and K-Theory [electronic resource] |
Author(s): |
Joseph Gubeladze Winfried Bruns |
Date: | 2009 |
Edition: | 1 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, thealgebras derived from the m, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphismproblems and automorphism groups, homological prope rties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. Thismonograph has been written with a view towards graduate students and resear chers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, alsospecialists in lattice polytopes and related objects will find an up-to-date discussion of affine m onoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructiveapproach wherever possible. Winfried Bruns is Professor of Mathematics at Universitt Osnabrck. Joseph Gubeladze is Professor of Mathematics at San Francisco State University |
Note: | Springer eBooks |
Contents: | Preface |
Polytopes, cones, and complexes | |
Affine monoids and their Hilbert bases | |
Multiples of lattice polytopes | |
Monoid algebras | |
Isomorphisms and automorphisms | |
Homological properties and Hilbert functions | |
Grbner bases, triangulations, and Koszul algebras | |
Projective modules over monoid rings | |
Bass | |
Whitehead groups of monoid rings | |
Varieties | |
References | |
Notation | |
Index | |
ISBN: | 9780387763569 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Springer Monographs in Mathematics, 1439-7382 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Algebra , K-theory , Discrete groups |
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Call number: | SPRINGER-2009-9780387724768:ONLINE Show nearby items on shelf |
Title: | A Course in Commutative Banach Algebras [electronic resource] |
Author(s): |
Eberhard Kaniuth |
Date: | 2009 |
Publisher: | New York, NY : Springer New York |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | Requiring only a basic knowledge of functional analysis, topology, complex analysis, measure theory and group theory, this book provides a thorough and self-contained introduction to the theory of commutative Banach algebras. Thecore are chapters on Gelfand's theory, regularity and spectral synthesis. Special emphasis is placed on applications in abstract harmonic analysis and on treating many special classes of commutative Banach algebras, such as uniformalgebras, group algebras and Beurling algebra s, and tensor products. Detailed proofs and a variety of exercises are given. The book aims at graduate students and can be used as a text for courses on Banach algebras, with variouspossible specializations, or a Gelfand theory based course in harmonic a nalysis |
Note: | Springer eBooks |
Contents: | Preface |
General Theory of Banach Algebras | |
Gelfand Theory | |
Functional Calculus, Shilov Boundary, and Applications | |
Regularity and Related Properties | |
Spectral Synthesis and Ideal Theory | |
Appendix | |
References | |
Index | |
ISBN: | 9780387724768 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Graduate Texts in Mathematics, 0072-5285 : v246 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Operator theory |
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Call number: | SPRINGER-2008-9783764387266:ONLINE Show nearby items on shelf |
Title: | Commutative Algebras of Toeplitz Operators on the Bergman Space [electronic resource] |
Author(s): |
Nikolai L Vasilevski |
Date: | 2008 |
Publisher: | Basel : Birkhuser Basel |
Size: | 1 online resource |
Note: | Springer e-book platform |
Note: | Springer 2013 e-book collections |
Note: | This book is devoted to the spectral theory of commutative C*-algebras of Toeplitz operators on the Bergman space and its applications. For each such commutative algebra there is a unitary operator which reduces Toeplitzoperators from this algebra to certain multiplication operators, thus providing their spectral type representations. This yields a powerful research tool giving direct access to the majority of the important properties of the Toeplitzoperators studied herein, such as boundedness, comp actness, spectral properties, invariant subspaces. The presence and exploitation of these spectral type representations forms the core for many results presented in the book. Amongother results it contains a criterion of when the algebras are commutative on each commonly considered weighted Bergman space together with their explicit descriptions a systematic study of Toeplitz operators with unbounded symbols aclarification of the difference between compactness of commutators and semi-commutators of Toepli tz operators the theory of Toeplitz and related operators with symbols having more than two limit values at boundary points and a kindof semi-classical analysis of spectral properties of Toeplitz operators. The book is addressed to a wide audience of math ematicians, from graduate students to researchers, whose primary interests lie in complex analysis and operatortheory |
Note: | Springer eBooks |
Contents: | 1. Prologue |
2. Bergman and Poly | |
Bergman Spaces | |
3. Bergman | |
Type Spaces on the Unit Disk | |
4. Toeplitz Operators with Commutative Symbol Algebras | |
5. Toeplitz Operators on the Unit Disk with Radial Symbols | |
6. Toeplitz Operators with Homogeneous Symbols | |
7. Anatomy of the Algebra Generated by Toeplitz Operators | |
8. Toeplitz Operators and Hyperbolic Geometry | |
9. Weighted Bergman spaces | |
10. Commutative Algebras of Toeplitz Operators | |
11. Dynamics of Properties, Radial Symbols | |
12. Dynamics of Properties, Parabolic case | |
13. Dynamics of Properties, Hyperbolic case | |
Appen | |
ISBN: | 9783764387266 |
Series: | e-books |
Series: | SpringerLink (Online service) |
Series: | Operator Theory: Advances and Applications : v185 |
Series: | Mathematics and Statistics (Springer-11649) |
Keywords: | Mathematics , Functional analysis , Functions of complex variables , Operator theory |
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