Rings and Categories of Modules
Rings and Categories of Modules
复制标题
DOI：
10.1007/978-1-4612-4418-9
复制
发表时间：
1974
期刊：
影响因子：
--
通讯作者：
F. W. Anderson;K. Fuller
中科院分区：
文献类型：
--
作者：
F. W. Anderson;K. Fuller
这本书的目的是提供一个合理的自成一体的帐户的一个主要部分的一般理论的戒指和模块适合作为一个文本的介绍和更先进的研究生课程。我们假设熟悉通常在标准本科代数课程中获得的环。我们的一般方法是绝对的，而不是算术的。文本的持续主题是研究环可能具有的单侧理想结构与其模块范畴的行为之间的关系。以下简要概述了集理论和范畴的基础，正文开始的基本定义和性质的环，模块和同态和范围通过全面的治疗直接和，有限性条件，韦德伯恩，阿廷定理，雅克布森根，霍姆和张量函数，森田等价和对偶，德组成理论的内射和投射模块，和半完善和完善的戒指。在这第二版中，我们已经包括了一章包含许多经典的结果，对阿丁尼亚环，hdped形成的基础上，许多当代研究的代表理论的阿丁尼亚环和有限维代数。为了说明和扩展课文，我们包括了大量的练习，涵盖了广泛的难度。当然，有许多环和模理论的重要领域是本文没有触及的。
This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.