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 id...(展开全部)

《国外数学名著系列(续1)(影印版)37:同调代数方法(第2版)》主要内容：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...(展开全部)

《国外数学名著系列(续1)(影印版)37:同调代数方法(第2版)》主要内容：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...(展开全部)

Sergei I. Gelfand American Mathematical Society, Providence, USA Yuri I. Manin Max Planck Institute for Mathematics, Bonn, Germany

《同调代数(英文)》主要内容简介：During the last decade the methods of algebraic topology have invaded extensively the domain of pure algebra, and initiated a number of internal revolutions. The purpose of this book is to present a unified account of these developments and to lay the foundations of a full-fledged theory. The invasion of algebra has occurred on three fronts through the construc...(展开全部)

We have inserted, in this edition, an extra chapter (Chapter X) entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological alge...(展开全部)

同调代数的思想方法主要来自代数拓

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 alg...(展开全部)

本书对读者的起点要求不高，是沿着一条非常简捷的途径，将读者带到本学科的前沿。本书主要内容包括:环与模、整性、诺特环与阿廷环、诺特环与整性、准素分解、张量积、平坦性、代数集、分次环与形式完备化、维数理论、范畴、阿贝尔范畴、同调、深度、正规环与正则环、微分与光滑性、带算子的群，本书每章后都附有若干习题，这些都是作者在教学中积累的。 本书可供高校有关师生阅读，也可作为研究生教材。

交换代数与同调代数是代数学中的重要领域，也是代数几何、代数数论等领域的强大工具，因此是很多不同方向的研究生和研究人员所需要甚至必备的。本书针对各方面读者的基本需要，内容包括多重线性代数、交换代数(包括“硬交换代数”)与同调代数等方面的基本理论，在取材上只注意这些学科中最重要且实用的基本内容，而不涉及很专门的课题。在内容的安排上，采取了“低起点，高坡度”的方式。在预备知识方面，只假定读者学过群论和域论(包括伽罗华理论)，而从环的基本理论讲起。每一章后面都有若干习题，标有星号的习题在附录B中有解答或提示。