An Introduction to Homological Algebra

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Publisher : Cambridge University Press
ISBN 13 : 113964307X
Total Pages : 470 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis An Introduction to Homological Algebra by : Charles A. Weibel

Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.

An Introduction to Homological Algebra

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Author :
Publisher : Cambridge University Press
ISBN 13 : 9780521058414
Total Pages : 294 pages
Book Rating : 4.0/5 (584 download)

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Book Synopsis An Introduction to Homological Algebra by : Northcott

Download or read book An Introduction to Homological Algebra written by Northcott and published by Cambridge University Press. This book was released on 1960 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra, because of its fundamental nature, is relevant to many branches of pure mathematics, including number theory, geometry, group theory and ring theory. Professor Northcott's aim is to introduce homological ideas and methods and to show some of the results which can be achieved. The early chapters provide the results needed to establish the theory of derived functors and to introduce torsion and extension functors. The new concepts are then applied to the theory of global dimensions, in an elucidation of the structure of commutative Noetherian rings of finite global dimension and in an account of the homology and cohomology theories of monoids and groups. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. This book is designed with the needs and problems of the beginner in mind, providing a helpful and lucid account for those about to begin research, but will also be a useful work of reference for specialists. It can also be used as a textbook for an advanced course.

Methods of Homological Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 3662032201
Total Pages : 388 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Methods of Homological Algebra by : Sergei I. Gelfand

Download or read book Methods of Homological Algebra written by Sergei I. Gelfand and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.

A Course in Homological Algebra

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Publisher : Springer Science & Business Media
ISBN 13 : 146849936X
Total Pages : 348 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis A Course in Homological Algebra by : P.J. Hilton

Download or read book A Course in Homological Algebra written by P.J. Hilton and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.

Lecture Notes in Algebraic Topology

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Publisher : American Mathematical Society
ISBN 13 : 1470473682
Total Pages : 385 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lecture Notes in Algebraic Topology by : James F. Davis

Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Homological Theory of Representations

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Publisher : Cambridge University Press
ISBN 13 : 1108985815
Total Pages : 518 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Homological Theory of Representations by : Henning Krause

Download or read book Homological Theory of Representations written by Henning Krause and published by Cambridge University Press. This book was released on 2021-11-18 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these methods from their foundations up and discusses several landmark results that illustrate their power and beauty. Categorical foundations include abelian and derived categories, with an emphasis on localisation, spectra, and purity. The representation theoretic focus is on module categories of Artin algebras, with discussions of the representation theory of finite groups and finite quivers. Also covered are Gorenstein and quasi-hereditary algebras, including Schur algebras, which model polynomial representations of general linear groups, and the Morita theory of derived categories via tilting objects. The final part is devoted to a systematic introduction to the theory of purity for locally finitely presented categories, covering pure-injectives, definable subcategories, and Ziegler spectra. With its clear, detailed exposition of important topics in modern representation theory, many of which were unavailable in one volume until now, it deserves a place in every representation theorist's library.

Introduction To Commutative Algebra

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Publisher : CRC Press
ISBN 13 : 0429973268
Total Pages : 140 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah

Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Relative Homological Algebra

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Publisher : Walter de Gruyter
ISBN 13 : 3110215217
Total Pages : 377 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Relative Homological Algebra by : Edgar E. Enochs

Download or read book Relative Homological Algebra written by Edgar E. Enochs and published by Walter de Gruyter. This book was released on 2011-10-27 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. In this new edition the authors have added well-known additional material in the first three chapters, and added new material that was not available at the time the original edition was published. In particular, the major changes are the following: Chapter 1: Section 1.2 has been rewritten to clarify basic notions for the beginner, and this has necessitated a new Section 1.3. Chapter 3: The classic work of D. G. Northcott on injective envelopes and inverse polynomials is finally included. This provides additional examples for the reader. Chapter 11: Section 11.9 on Kaplansky classes makes volume one more up to date. The material in this section was not available at the time the first edition was published. The authors also have clarified some text throughout the book and updated the bibliography by adding new references. The book is also suitable for an introductory course in commutative and ordinary homological algebra.

Categorical Homotopy Theory

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Publisher : Cambridge University Press
ISBN 13 : 1139952633
Total Pages : 371 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Categorical Homotopy Theory by : Emily Riehl

Download or read book Categorical Homotopy Theory written by Emily Riehl and published by Cambridge University Press. This book was released on 2014-05-26 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

Homology Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461208815
Total Pages : 258 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Homology Theory by : James W. Vick

Download or read book Homology Theory written by James W. Vick and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.

Introduction to Homological Algebra, 85

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Publisher : Academic Press
ISBN 13 : 0080874010
Total Pages : 393 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Introduction to Homological Algebra, 85 by : Joseph J. Rotman

Download or read book Introduction to Homological Algebra, 85 written by Joseph J. Rotman and published by Academic Press. This book was released on 1979-09-07 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Homological Algebra discusses the origins of algebraic topology. It also presents the study of homological algebra as a two-stage affair. First, one must learn the language of Ext and Tor and what it describes. Second, one must be able to compute these things, and often, this involves yet another language: spectral sequences. Homological algebra is an accessible subject to those who wish to learn it, and this book is the author's attempt to make it lovable. This book comprises 11 chapters, with an introductory chapter that focuses on line integrals and independence of path, categories and functors, tensor products, and singular homology. Succeeding chapters discuss Hom and ?; projectives, injectives, and flats; specific rings; extensions of groups; homology; Ext; Tor; son of specific rings; the return of cohomology of groups; and spectral sequences, such as bicomplexes, Kunneth Theorems, and Grothendieck Spectral Sequences. This book will be of interest to practitioners in the field of pure and applied mathematics.

An Elementary Approach to Homological Algebra

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Publisher : CRC Press
ISBN 13 : 0203484088
Total Pages : 326 pages
Book Rating : 4.2/5 (34 download)

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Book Synopsis An Elementary Approach to Homological Algebra by : L.R. Vermani

Download or read book An Elementary Approach to Homological Algebra written by L.R. Vermani and published by CRC Press. This book was released on 2003-05-28 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Often perceived as dry and abstract, homological algebra nonetheless has important applications in a number of important areas, including ring theory, group theory, representation theory, and algebraic topology and geometry. Although the area of study developed almost 50 years ago, a textbook at this level has never before been available. An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning graduate students, the author presents the material in a clear, easy-to-understand manner with many examples and exercises. The book's level of detail, while not exhaustive, also makes it useful for self-study and as a reference for researchers.

Homological Algebra

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Publisher : World Scientific
ISBN 13 : 9814425923
Total Pages : 356 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Homological Algebra by : Marco Grandis

Download or read book Homological Algebra written by Marco Grandis and published by World Scientific. This book was released on 2013 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a study of semi-exact homological categories as a basis for a generalized homological algebra. The aim is to extend homological notions to deeply non-abelian situations, where satellites and spectral sequences produced by unstable homotopy can still be studied.

The Atiyah-Singer Index Theorem

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Publisher : Springer
ISBN 13 : 3540359214
Total Pages : 230 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Atiyah-Singer Index Theorem by : P. Shanahan

Download or read book The Atiyah-Singer Index Theorem written by P. Shanahan and published by Springer. This book was released on 2006-11-15 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Homology

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Publisher : Springer Science & Business Media
ISBN 13 : 3642620299
Total Pages : 436 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Homology by : Saunders MacLane

Download or read book Homology written by Saunders MacLane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

An Introduction to Algebraic Topology

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Publisher : Springer Science & Business Media
ISBN 13 : 1461245761
Total Pages : 447 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis An Introduction to Algebraic Topology by : Joseph J. Rotman

Download or read book An Introduction to Algebraic Topology written by Joseph J. Rotman and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Trivial Extensions of Abelian Categories

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Publisher : Springer
ISBN 13 : 3540374876
Total Pages : 133 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Trivial Extensions of Abelian Categories by : R.M. Fossum

Download or read book Trivial Extensions of Abelian Categories written by R.M. Fossum and published by Springer. This book was released on 2006-11-15 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: