A First Course Of 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 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.
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.
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.
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.
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.
An Elementary Approach To Homological Algebra
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Author : L.R. Vermani
language : en
Publisher: CRC Press
Release Date : 2003-05-28
An Elementary Approach To Homological Algebra written by L.R. Vermani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-28 with Mathematics categories.
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.
Cohomology Of Groups
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Author : Kenneth S. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Cohomology Of Groups written by Kenneth S. Brown 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.
As a second year graduate textbook, Cohomology of Groups introduces students to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology. The basics of the subject are given (along with exercises) before the author discusses more specialized topics.
Relative Homological Algebra
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Author : Edgar E. Enochs
language : en
Publisher: Walter de Gruyter
Release Date : 2011-10-27
Relative Homological Algebra written by Edgar E. Enochs and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-27 with Mathematics categories.
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.