A Course In Homological Algebra

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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.

A Course In Homological Algebra

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Author : Peter J. Hilton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-05

A Course In Homological Algebra written by Peter 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 2012-09-05 with Mathematics categories.

We have inserted, in this edition, an extra chapter (Chapter X) entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological algebra to other parts of algebra. Most of the material presented in these four sections was not available when this text was first published. Naturally, the treatments in these five sections are somewhat cursory, the intention being to give the flavor of the homo logical methods rather than the details of the arguments and results. We would like to express our appreciation of help received in writing Chapter X; in particular, to Ross Geoghegan and Peter Kropholler (Section 3), and to Jacques Thevenaz (Sections 4 and 5). The only other changes consist of the correction of small errors and, of course, the enlargement of the Index. Peter Hilton Binghamton, New York, USA Urs Stammbach Zurich, Switzerland Contents Preface to the Second Edition vii Introduction. . I. Modules.

Basic Homological Algebra

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Author : M. Scott Osborne
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Basic Homological Algebra written by M. Scott Osborne 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 2012-12-06 with Mathematics categories.

Five years ago, I taught a one-quarter course in homological algebra. I discovered that there was no book which was really suitable as a text for such a short course, so I decided to write one. The point was to cover both Ext and Tor early, and still have enough material for a larger course (one semester or two quarters) going off in any of several possible directions. This book is 'also intended to be readable enough for independent study. The core of the subject is covered in Chapters 1 through 3 and the first two sections ofChapter 4. At that point there are several options. Chapters 4 and 5 cover the more traditional aspects of dimension and ring changes. Chapters 6 and 7 cover derived functors in general. Chapter 8 focuses on a special property of Tor. These three groupings are independent, as are various sections from Chapter 9, which is intended as a source of special topics. (The prerequisites for each section of Chapter 9 are stated at the beginning.) Some things have been included simply because they are hard to find else where, and they naturally fit into the discussion. Lazard's theorem (Section 8.4)-is an example; Sections4,5, and 7ofChapter 9 containother examples, as do the appendices at the end.

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.

A First Course Of Homological Algebra

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Author : Douglas Geoffrey Northcott
language : en
Publisher: CUP Archive
Release Date : 1973-10-11

A First Course Of Homological Algebra written by Douglas Geoffrey Northcott and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973-10-11 with Mathematics categories.

Designed to introduce the student to homological algebra avoiding the elaborate machinery usually associated with the subject.

A Course In Homological Algebra

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Author : Peter John Hilton
language : en
Publisher:
Release Date : 1971

A Course In Homological Algebra written by Peter John Hilton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Algebra, Homological categories.

A Course In Homological Algebra

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Author : Peter John Hilton
language : en
Publisher:
Release Date : 1971

A Course In Homological Algebra written by Peter John Hilton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Algebra homológica categories.

An Introduction To Homological Algebra

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Author : Douglas Geoffrey Northcott
language : en
Publisher:
Release Date : 2003-01-01

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 2003-01-01 with Homology theory categories.

Homology Theory

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Author : James W. Vick
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-01-07

Homology Theory written by James W. Vick 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 1994-01-07 with Mathematics categories.

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.

A Course In Homological Algebra

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Author : Peter John Hilton (Mathematician, Great Britain)
language : en
Publisher:
Release Date : 1971

A Course In Homological Algebra written by Peter John Hilton (Mathematician, Great Britain) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Algebra, Homological categories.