Relative Homological Algebra

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Relative Homological Algebra

Author : Edgar E. Enochs
Publisher : Walter de Gruyter
ISBN 13 : 3110215217
Total Pages : 377 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Relative Homological Algebra by : Edgar E. Enochs

Download or read book Relative Homological Algebra written by Edgar E. Enochs and published by Walter de Gruyter. This book was released on 2011-10-27 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Relative Homological Algebra

Author : Edgar E. Enochs
Publisher : Walter de Gruyter
ISBN 13 : 3110215233
Total Pages : 109 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Relative Homological Algebra by : Edgar E. Enochs

Download or read book Relative Homological Algebra written by Edgar E. Enochs and published by Walter de Gruyter. This book was released on 2011-08-29 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Relative Homological Algebra

Author : Samuel Eilenberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821812556
Total Pages : 43 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Foundations of Relative Homological Algebra by : Samuel Eilenberg

Download or read book Foundations of Relative Homological Algebra written by Samuel Eilenberg and published by American Mathematical Soc.. This book was released on 1965 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main notion of this paper is that of a "projective class of sequences" in an arbitrary (pointed) category. Each such class carries with it its own projective objects. One can then talk about projective resolutions, and if the category is additive, all the usual properties of the resolutions hold. In particular, this will permit the development of homological algebra in some additive categories which are not abelian, e.g., the category of comodules over a coalgebra over an arbitrary commutative ring.

Foundations of Relative Homological Algebra

Author : Samuel Eilenberg
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (256 download)

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Book Synopsis Foundations of Relative Homological Algebra by : Samuel Eilenberg

Download or read book Foundations of Relative Homological Algebra written by Samuel Eilenberg and published by . This book was released on 1966 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Homological Algebra

Author : Charles A. Weibel
Publisher : Cambridge University Press
ISBN 13 : 113964307X
Total Pages : 470 pages
Book Rating : 4.1/5 (396 download)

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Book Synopsis An Introduction to Homological Algebra by : Charles A. Weibel

Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gorenstein Homological Algebra

Author : Alina Iacob
Publisher : CRC Press
ISBN 13 : 1351660268
Total Pages : 214 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Gorenstein Homological Algebra by : Alina Iacob

Download or read book Gorenstein Homological Algebra written by Alina Iacob and published by CRC Press. This book was released on 2018-08-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gorenstein homological algebra is an important area of mathematics, with applications in commutative and noncommutative algebra, model category theory, representation theory, and algebraic geometry. While in classical homological algebra the existence of the projective, injective, and flat resolutions over arbitrary rings are well known, things are a little different when it comes to Gorenstein homological algebra. The main open problems in this area deal with the existence of the Gorenstein injective, Gorenstein projective, and Gorenstein flat resolutions. Gorenstein Homological Algebra is especially suitable for graduate students interested in homological algebra and its applications.

Homology

Author : Saunders MacLane
Publisher : Springer Science & Business Media
ISBN 13 : 3642620299
Total Pages : 436 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Homology by : Saunders MacLane

Download or read book Homology written by Saunders MacLane and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Homological Algebra of Semimodules and Semicontramodules

Author : Leonid Positselski
Publisher : Springer Science & Business Media
ISBN 13 : 303460436X
Total Pages : 352 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Homological Algebra of Semimodules and Semicontramodules by : Leonid Positselski

Download or read book Homological Algebra of Semimodules and Semicontramodules written by Leonid Positselski and published by Springer Science & Business Media. This book was released on 2010-09-02 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive coverage on semi-infinite homology and cohomology of associative algebraic structures. It features rich representation-theoretic and algebro-geometric examples and applications.

Homotopical Algebra

Author : Daniel G. Quillen
Publisher : Springer
ISBN 13 : 3540355235
Total Pages : 165 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Homotopical Algebra by : Daniel G. Quillen

Download or read book Homotopical Algebra written by Daniel G. Quillen and published by Springer. This book was released on 2006-11-14 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Author : Marco A. P. Bullones
Publisher : CRC Press
ISBN 13 : 149872535X
Total Pages : 370 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Introduction to Abelian Model Structures and Gorenstein Homological Dimensions by : Marco A. P. Bullones

Download or read book Introduction to Abelian Model Structures and Gorenstein Homological Dimensions written by Marco A. P. Bullones and published by CRC Press. This book was released on 2016-08-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Abelian Model Structures and Gorenstein Homological Dimensions provides a starting point to study the relationship between homological and homotopical algebra, a very active branch of mathematics. The book shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The first part of the book introduces the definitions and notations of the universal constructions most often used in category theory. The next part presents a proof of the Eklof and Trlifaj theorem in Grothedieck categories and covers M. Hovey’s work that connects the theories of cotorsion pairs and model categories. The final two parts study the relationship between model structures and classical and Gorenstein homological dimensions and explore special types of Grothendieck categories known as Gorenstein categories. As self-contained as possible, this book presents new results in relative homological algebra and model category theory. The author also re-proves some established results using different arguments or from a pedagogical point of view. In addition, he proves folklore results that are difficult to locate in the literature.

Handbook of Algebra

Author :
Publisher : Elsevier
ISBN 13 : 0080532950
Total Pages : 936 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Handbook of Algebra by :

Download or read book Handbook of Algebra written by and published by Elsevier. This book was released on 1995-12-18 with total page 936 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

Lecture Notes in Algebraic Topology

Author : James F. Davis
Publisher : American Mathematical Society
ISBN 13 : 1470473682
Total Pages : 385 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lecture Notes in Algebraic Topology by : James F. Davis

Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Relative Homological Algebra and Homological Dimension of Lie Algebras

Author : Byoung-Song Chwe
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (29 download)

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Book Synopsis Relative Homological Algebra and Homological Dimension of Lie Algebras by : Byoung-Song Chwe

Download or read book Relative Homological Algebra and Homological Dimension of Lie Algebras written by Byoung-Song Chwe and published by . This book was released on 1961 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Abelian Model Structures and Gorenstein Homological Dimensions

Author : Marco A. P. Bullones
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781498725347
Total Pages : 0 pages
Book Rating : 4.7/5 (253 download)

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Book Synopsis Introduction to Abelian Model Structures and Gorenstein Homological Dimensions by : Marco A. P. Bullones

Download or read book Introduction to Abelian Model Structures and Gorenstein Homological Dimensions written by Marco A. P. Bullones and published by Chapman & Hall/CRC. This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a starting point to study the relationship between homological and homotopical algebra. It shows how to obtain new model structures in homological algebra by constructing a pair of compatible complete cotorsion pairs related to a specific homological dimension and then applying the Hovey Correspondence to generate an abelian model structure. The book presents new results in relative homological algebra and model category theory, re-proves some established results, and proves folklore results that are difficult to find in the literature.

Abelian Groups, Rings, Modules, and Homological Algebra

Author : Pat Goeters
Publisher : CRC Press
ISBN 13 : 142001076X
Total Pages : 354 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Abelian Groups, Rings, Modules, and Homological Algebra by : Pat Goeters

Download or read book Abelian Groups, Rings, Modules, and Homological Algebra written by Pat Goeters and published by CRC Press. This book was released on 2016-04-19 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: About the book In honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par

An Elementary Approach to Homological Algebra

Author : L.R. Vermani
Publisher : CRC Press
ISBN 13 : 0203484088
Total Pages : 328 pages
Book Rating : 4.2/5 (34 download)

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Book Synopsis An Elementary Approach to Homological Algebra by : L.R. Vermani

Download or read book An Elementary Approach to Homological Algebra written by L.R. Vermani and published by CRC Press. This book was released on 2003-05-28 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Commutative Algebra

Author : Michael F. Atiyah
Publisher : CRC Press
ISBN 13 : 0429973268
Total Pages : 140 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah

Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.