| 书目名称 | Rings and Categories of Modules | | 编辑 | Frank W. Anderson,Kent R. Fuller | | 视频video | | | 丛书名称 | Graduate Texts in Mathematics | | 图书封面 |  | | 描述 | 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-Art in Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semiperfect and perfect rings. 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 theo | | 出版日期 | Textbook 19741st edition | | 关键词 | Area; Categories; Division; Finite; Modules; Rings; algebra; behavior; density; duality; functions; homomorphis | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4684-9913-1 | | isbn_ebook | 978-1-4684-9913-1Series ISSN 0072-5285 Series E-ISSN 2197-5612 | | issn_series | 0072-5285 | | copyright | Springer Science+Business Media New York 1974 |
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发表于 2025-3-21 18:25:26
