{"product_id":"an-introduction-to-homological-algebra-paperback-1","title":"An Introduction to Homological Algebra - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eJoseph J. Rotman\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eLearning homological algebra is 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. This book gives a treatment of homological algebra which motivates 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, contrasting it with homological algebra.\u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWith a wealth of examples as well as abundant applications to Algebra, this is a must-read work: a clearly written, easy-to-follow guide to Homological Algebra. The author provides a treatment of Homological Algebra which approaches the subject in terms of its origins in algebraic topology. In this brand new edition the text has been fully updated and revised throughout and new material on sheaves and abelian categories has been added.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eApplications include the following: \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e* to rings -- Lazard's theorem that flat modules are direct limits of free modules, Hilbert's Syzygy Theorem, Quillen-Suslin's solution of Serre's problem about projectives over polynomial rings, Serre-Auslander-Buchsbaum characterization of regular local rings (and a sketch of unique factorization);\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e* to groups -- Schur-Zassenhaus, Gaschutz's theorem on outer automorphisms of finite p-groups, Schur multiplier, cotorsion groups;\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e* to sheaves -- sheaf cohomology, Cech cohomology, discussion of Riemann-Roch Theorem over compact Riemann surfaces.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eLearning Homological Algebra is a two-stage affair. Firstly, one must learn the language of Ext and Tor, and what this describes. Secondly, one must be able to compute these things using a separate language: that of spectral sequences. The basic properties of spectral sequences are developed using exact couples. All is done in the context of bicomplexes, for almost all applications of spectral sequences involve indices. Applications include Grothendieck spectral sequences, change of rings, Lyndon-Hochschild-Serre sequence, and theorems of Leray and Cartan computing sheaf cohomology.\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003eJoseph Rotman is Professor Emeritus of Mathematics at the University of Illinois at Urbana-Champaign. He is the author of numerous successful textbooks, including Advanced Modern Algebra (Prentice-Hall 2002), Galois Theory, 2nd Edition (Springer 1998) A First Course in Abstract Algebra (Prentice-Hall 1996), Introduction to the Theory of Groups, 4th Edition (Springer 1995), and Introduction to Algebraic Topology (Springer 1988).\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 710\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 1.4 x 9.1 x 5.9 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eIllustrated:\u003c\/strong\u003e Yes\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e October 14, 2008\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":52704485835059,"sku":"9780387245270","price":136.58,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0300\/5595\/6612\/files\/MlBZOEVadytOWnVPUERYbEJJSERxQT09_9c9be8fa-8bdd-4eef-a724-aa6df8af3aa7.webp?v=1763355544","url":"https:\/\/www.vysn.com\/en-ca\/products\/an-introduction-to-homological-algebra-paperback-1","provider":"VYSN","version":"1.0","type":"link"}