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. Rotman is a renowned textbook author in contemporary mathematics. Over the past four decades, he has published numerous successful texts of introductory character, mainly in the field of modern abstract algebra and its related disciplines.
While the first edition covered exclusively aspects of the homological algebra of groups, rings, and modules, that is, topics from its first period of development, the new edition includes some additional material from the second period, together with numerous other, more recent results from the homological algebra of groups, rings, and modules.
The new edition has almost doubled in size and represents a substantial updating of the classic original. The book is mainly concerned with homological algebra in module categories ….
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New Releases. Categories: Mathematics Mathematical Foundations Algebra. An Introduction to Homological Algebra. Description 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.
It contains many references for further study and also to original sources. A final section is devoted to comments on the various chapters, supplementary notes and suggestions for further reading. Over the past four decades, he has published numerous successful texts of introductory character, mainly in the field of modern abstract algebra and its related disciplines. Rotman 1 1. Asked 10 months ago.
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. Product details Format Paperback pages Dimensions x x Other books in this series.
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His e-mail address is fzc oso. Preface to the second edition. Skip to main content.
Library of Congress Cataloging-in-Publication Data. Weibel, Charles A., An introduction to homological algebra / Charles A. Weibel. Charles A. Weibel, Rutgers University, New Jersey. Subjects: Algebra, Real and Complex Analysis, Recreational Mathematics, Mathematics. 8 - Simplicial Methods in Homological Algebra.
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