An Introduction To Homological Algebra
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An Introduction To Homological Algebra
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Author : Joseph J. Rotman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-10
An Introduction To Homological Algebra written by Joseph J. Rotman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-10 with Mathematics categories.
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.
An Introduction To Homological Algebra
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Author : Charles A. Weibel
language : en
Publisher: Cambridge University Press
Release Date : 1995-10-27
An Introduction To Homological Algebra written by Charles A. Weibel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-27 with Mathematics categories.
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.
Introduction To Homological Algebra 85
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Author : Joseph J. Rotman
language : en
Publisher: Academic Press
Release Date : 1979-09-07
Introduction To Homological Algebra 85 written by Joseph J. Rotman and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-09-07 with Mathematics categories.
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 X; 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 Introduction To Homological Algebra
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Author :
language : en
Publisher:
Release Date : 1979
An Introduction To Homological Algebra written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
An Introduction To Homological Algebra
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Author : Douglas Geoffrey Northcott
language : en
Publisher:
Release Date : 1960
An Introduction To Homological Algebra written by Douglas Geoffrey Northcott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematics categories.
This book is designed with the needs and problems of the beginner in mind, but will also be a useful work of reference for specialists.
Introduction To Homological Algebra
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Author : Sze-Tsen Hu
language : en
Publisher:
Release Date : 1968
Introduction To Homological Algebra written by Sze-Tsen Hu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
An Introduction To Homological Algebra
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Author :
language : en
Publisher:
Release Date : 1962
An Introduction To Homological Algebra written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with categories.
A Course In Homological Algebra
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Author : P.J. Hilton
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
A Course In Homological Algebra written by P.J. Hilton and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Methods Of Homological Algebra
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Author : Sergei I. Gelfand
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Methods Of Homological Algebra written by Sergei I. Gelfand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
An Introduction To Homological Algebra
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Author : Douglas Geoffrey Northcott
language : en
Publisher:
Release Date : 1962
An Introduction To Homological Algebra written by Douglas Geoffrey Northcott and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with categories.