Basic Homological Algebra

Author: M. Scott Osborne

Publisher: Springer Science & Business Media

ISBN: 1461212782

Category: Mathematics

Page: 398

View: 2094

DOWNLOAD NOW »

From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especially appreciated the lively style of the book; [...] one is quickly able to find necessary details." EMS Newsletter
Release

Basic Commutative Algebra

Author: Balwant Singh

Publisher: World Scientific

ISBN: 9814313629

Category: Mathematics

Page: 390

View: 3806

DOWNLOAD NOW »

This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained. The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.
Release

An Introduction to Homological Algebra

Author: Joseph J. Rotman

Publisher: Springer Science & Business Media

ISBN: 0387683240

Category: Mathematics

Page: 710

View: 7096

DOWNLOAD NOW »

Graduate mathematics students will find this book an easy-to-follow, step-by-step guide to the subject. Rotman’s book gives a treatment of homological algebra which approaches the subject in terms of its origins in algebraic topology. In this new edition the book has been updated and revised throughout and new material on sheaves and cup products has been added. The author has also included material about homotopical algebra, alias K-theory. Learning homological algebra is a two-stage affair. First, one must learn the language of Ext and Tor. Second, one must be able to compute these things with spectral sequences. Here is a work that combines the two.
Release

Introduction to Algebraic Geometry and Commutative Algebra

Author: Dilip P. Patil,Uwe Storch

Publisher: World Scientific

ISBN: 9814304573

Category: Mathematics

Page: 207

View: 9406

DOWNLOAD NOW »

Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.
Release

Representations of Finite Groups: Local Cohomology and Support

Author: David J. Benson,Srikanth Iyengar,Henning Krause

Publisher: Springer Science & Business Media

ISBN: 3034802609

Category: Mathematics

Page: 105

View: 1449

DOWNLOAD NOW »

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 from commutative algebra, cohomology 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 Daniel Quillen’s description of the algebraic variety corresponding 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 of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf 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 of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Release

Introduction to Commutative Algebra and Algebraic Geometry

Author: Ernst Kunz

Publisher: Springer Science & Business Media

ISBN: 1461459877

Category: Mathematics

Page: 238

View: 850

DOWNLOAD NOW »

Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative 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 representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
Release

Relative Homological Algebra

Author: Edgar E. Enochs

Publisher: Walter de Gruyter

ISBN: 3110215217

Category: Mathematics

Page: 372

View: 2012

DOWNLOAD NOW »

This is the second revised edition of an introduction to contemporary relative homological algebra. It supplies important material essential to understand topics in algebra, algebraic geometry and algebraic topology. Each section comes with exercises providing practice problems for students as well as additional important results for specialists. The book is also suitable for an introductory course in commutative and ordinary homological algebra.
Release

Six Lectures on Commutative Algebra

Author: J. Elias,J. M. Giral,Rosa M. Miró-Roig,Santiago Zarzuela

Publisher: Springer Science & Business Media

ISBN: 3034603290

Category: Mathematics

Page: 402

View: 3396

DOWNLOAD NOW »

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH
Release

Arithmetic of Blowup Algebras

Author: Wolmer V. Vasconcelos

Publisher: Cambridge University Press

ISBN: 9780521454841

Category: Mathematics

Page: 329

View: 9452

DOWNLOAD NOW »

This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.
Release