Methods Of Homological Algebra

Author : Sergei I. Gelfand,Yuri J. Manin
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662032206

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Methods of Homological Algebra by Sergei I. Gelfand,Yuri J. Manin Pdf

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.

Author : S.I. Gelfand,Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 55,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642579110

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Homological Algebra by S.I. Gelfand,Yu.I. Manin Pdf

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

Author : Charles A. Weibel
Publisher : Cambridge University Press
Page : 470 pages
File Size : 51,7 Mb
Release : 1995-10-27
Category : Mathematics
ISBN : 9781139643078

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An Introduction to Homological Algebra by Charles A. Weibel Pdf

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.

Author : Sergeĭ Izrailevich Gelʹfand,I︠U︡. I. Manin
Publisher : Springer Verlag
Page : 372 pages
File Size : 49,6 Mb
Release : 1996-01-01
Category : Mathematics
ISBN : 0387547460

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Methods of Homological Algebra by Sergeĭ Izrailevich Gelʹfand,I︠U︡. I. Manin Pdf

Author : P.J. Hilton,U. Stammbach
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 55,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781468499360

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A Course in Homological Algebra by P.J. Hilton,U. Stammbach Pdf

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.

Author : Sergei I. Gelfand,Yuri I. Manin
Publisher : Unknown
Page : 396 pages
File Size : 52,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662124939

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Methods of Homological Algebra by Sergei I. Gelfand,Yuri I. Manin Pdf

Author : Wolmer Vasconcelos
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 48,8 Mb
Release : 2004-05-18
Category : Mathematics
ISBN : 3540213112

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Computational Methods in Commutative Algebra and Algebraic Geometry by Wolmer Vasconcelos Pdf

This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.

Author : Henri Cartan,Samuel Eilenberg
Publisher : Princeton University Press
Page : 410 pages
File Size : 55,6 Mb
Release : 1999-12-19
Category : Mathematics
ISBN : 0691049912

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Homological Algebra by Henri Cartan,Samuel Eilenberg Pdf

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.

Author : Henning Krause
Publisher : Cambridge University Press
Page : 517 pages
File Size : 41,8 Mb
Release : 2021-11-18
Category : Mathematics
ISBN : 9781108838894

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Homological Theory of Representations by Henning Krause Pdf

This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.

Author : Northcott
Publisher : Cambridge University Press
Page : 294 pages
File Size : 43,5 Mb
Release : 1960
Category : Mathematics
ISBN : 0521058414

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An Introduction to Homological Algebra by Northcott Pdf

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.

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 49,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253501

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Commutative Algebra by David Eisenbud Pdf

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Author : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 55,5 Mb
Release : 2014-05-26
Category : Mathematics
ISBN : 9781107048454

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Categorical Homotopy Theory by Emily Riehl Pdf

This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.

Author : S.I. Gelfand,Yu.I. Manin
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 43,8 Mb
Release : 1994-03-29
Category : Mathematics
ISBN : 3540533737

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Homological Algebra by S.I. Gelfand,Yu.I. Manin Pdf

This book, the first printing of which was published as volume 38 of the Encyclopaedia of Mathematical Sciences, presents a modern approach to homological algebra, based on the systematic use of the terminology and ideas of derived categories and derived functors. The book contains applications of homological algebra to the theory of sheaves on topological spaces, to Hodge theory, and to the theory of modules over rings of algebraic differential operators (algebraic D-modules). The authors Gelfand and Manin explain all the main ideas of the theory of derived categories. Both authors are well-known researchers and the second, Manin, is famous for his work in algebraic geometry and mathematical physics. The book is an excellent reference for graduate students and researchers in mathematics and also for physicists who use methods from algebraic geometry and algebraic topology.

Author : Paul G. Goerss,John F. Jardine
Publisher : Birkhäuser
Page : 520 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887076

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Simplicial Homotopy Theory by Paul G. Goerss,John F. Jardine Pdf

Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.

Author : J.L. Bueso,José Gómez-Torrecillas,A. Verschoren
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 54,7 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9789401702850

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Algorithmic Methods in Non-Commutative Algebra by J.L. Bueso,José Gómez-Torrecillas,A. Verschoren Pdf

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.