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Titlebook: Rings and Categories of Modules; Frank W. Anderson,Kent R. Fuller Textbook 1992Latest edition Springer-Verlag New York, Inc. 1992 algebra.

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發(fā)表于 2025-3-21 17:54:36 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Rings and Categories of Modules
編輯Frank W. Anderson,Kent R. Fuller
視頻videohttp://file.papertrans.cn/831/830418/830418.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Rings and Categories of Modules;  Frank W. Anderson,Kent R. Fuller Textbook 1992Latest edition Springer-Verlag New York, Inc. 1992 algebra.
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-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 represent
出版日期Textbook 1992Latest edition
關(guān)鍵詞algebra; homomorphism; representation theory; ring; transformation
版次2
doihttps://doi.org/10.1007/978-1-4612-4418-9
isbn_softcover978-1-4612-8763-6
isbn_ebook978-1-4612-4418-9Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag New York, Inc. 1992
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沙發(fā)
發(fā)表于 2025-3-21 21:58:05 | 只看該作者
板凳
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Direct Sums and Products,ion about . by mining .. So in this chapter we start to probe more deeply into the structure of the modules themselves. In so far as possible we propose to do this in the context of the category . for in this way at any subsequent stage we shall be able to apply the general machinery of category theory.
地板
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Classical Ring-Structure Theorems,ful left module. In Section 14 we study rings characterized by this latter property—the “(left) primitive” rings. Here we prove Jacobson’s important generalization of the semisimple case characterizing left primitive rings as “dense rings” of linear transformations.
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發(fā)表于 2025-3-23 01:12:53 | 只看該作者
Textbook 1992Latest editionfor 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-side
9#
發(fā)表于 2025-3-23 04:42:02 | 只看該作者
Direct Sums and Products,, in general, . does not characterize .. However, as we shall see in Chapter 6 it does come close. Thus, we can expect to uncover substantial information about . by mining .. So in this chapter we start to probe more deeply into the structure of the modules themselves. In so far as possible we propo
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