# Search results for: an-introduction-to-homological-algebra

## An Introduction to Homological Algebra Author : Charles A. Weibel
File Size : 24.36 MB
Format : PDF, ePub, Mobi
A portrait of the subject of homological algebra as it exists today.

## An Introduction to Homological Algebra Author : Joseph J. Rotman
File Size : 81.59 MB
Format : PDF, Kindle
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.

## Introduction to Homological Algebra 85 Author : Joseph J. Rotman
File Size : 47.52 MB
Format : PDF, ePub
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 Author : Northcott
File Size : 23.47 MB
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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.

## An Introduction to Homological Algebra ICM Edition Author : Charles A. Weibel
File Size : 57.47 MB
Format : PDF, ePub, Mobi

## An introduction to homological algebra Author : Douglas G. Northcott
File Size : 49.84 MB
Format : PDF, Docs

## Homological Algebra Author : Henry Cartan
File Size : 65.23 MB
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When this book was written, methods of algebraic topology had caused revolutions in the world of pure algebra. To clarify the advances that had been made, Cartan and Eilenberg tried to unify the fields and to construct the framework of a fully fledged theory. The invasion of algebra had occurred on three fronts through the construction of cohomology theories for groups, Lie algebras, and associative algebras. This book presents a single homology (and also cohomology) theory that embodies all three; a large number of results is thus established in a general framework. Subsequently, each of the three theories is singled out by a suitable specialization, and its specific properties are studied. The starting point is the notion of a module over a ring. The primary operations are the tensor product of two modules and the groups of all homomorphisms of one module into another. From these, "higher order" derived of operations are obtained, which enjoy all the properties usually attributed to homology theories. This leads in a natural way to the study of "functors" and of their "derived functors." This mathematical masterpiece will appeal to all mathematicians working in algebraic topology.

## An Introduction to Homological Algebra Author :
File Size : 25.49 MB
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## An Introduction to Algebraic Topology Author : Joseph J. Rotman
File Size : 27.72 MB
Format : PDF, Mobi
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.

## An Elementary Approach to Homological Algebra Author : L.R. Vermani
File Size : 25.27 MB
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Homological algebra was developed as an area of study almost 50 years ago, and many books on the subject exist. However, few, if any, of these books are written at a level appropriate for students approaching the subject for the first time. An Elementary Approach to Homological Algebra fills that void. Designed to meet the needs of beginning

## Introduction to Categories Homological Algebra and Sheaf Cohomology Author : J. R. Strooker
File Size : 35.95 MB
Format : PDF, ePub, Mobi
Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical fields. This textbook provides an introduction to these methods, describing their elements and illustrating them by examples.

## A Singular Introduction to Commutative Algebra Author : Gert-Martin Greuel
File Size : 84.19 MB
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This substantially enlarged second edition aims to lead a further stage in the computational revolution in commutative algebra. This is the first handbook/tutorial to extensively deal with SINGULAR. Among the book’s most distinctive features is a new, completely unified treatment of the global and local theories. Another feature of the book is its breadth of coverage of theoretical topics in the portions of commutative algebra closest to algebraic geometry, with algorithmic treatments of almost every topic.

## Methods of Homological Algebra Author : Sergei I. Gelfand
File Size : 36.87 MB
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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. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.

## Homology Theory Author : P. J. Hilton
File Size : 59.67 MB
Format : PDF, Mobi
This account of algebraic topology is complete in itself, assuming no previous knowledge of the subject. It is used as a textbook for students in the final year of an undergraduate course or on graduate courses and as a handbook for mathematicians in other branches who want some knowledge of the subject.

## Foundations of Relative Homological Algebra Author : Samuel Eilenberg
File Size : 84.68 MB
Format : PDF, ePub

## Relative Homological Algebra Author : Edgar E. Enochs
File Size : 23.36 MB
Format : PDF
This second volume deals with the relative homological algebra of complexes of modules and their applications. It is a concrete and easy introduction to the kind of homological algebra which has been developed in the last 50 years. The book serves as a bridge between the traditional texts on homological algebra and more advanced topics such as triangulated and derived categories or model category structures. It addresses to readers who have had a course in classical homological algebra, as well as to researchers.

## Introduction to Homological Methods in Commutative Rings Author : A. V. Geramita
File Size : 70.86 MB
Format : PDF, ePub, Mobi

## An Algebraic Introduction to Complex Projective Geometry Author : Christian Peskine
File Size : 59.18 MB
Format : PDF, Mobi
In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.

## Cyclic Homology Author : Jean-Louis Loday
File Size : 68.4 MB
Format : PDF, ePub 