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Titlebook: Exercises in Modules and Rings; T. Y. Lam Book 2007 Springer-Verlag New York 2007 Division.Volume.matrix

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发表于 2025-3-21 18:32:17 | 显示全部楼层 |阅读模式
书目名称Exercises in Modules and Rings
编辑T. Y. Lam
视频video
概述Companion volume to GTM 189
丛书名称Problem Books in Mathematics
图书封面Titlebook: Exercises in Modules and Rings;  T. Y. Lam Book 2007 Springer-Verlag New York 2007 Division.Volume.matrix
描述The idea of writing this book came roughly at the time of publication of my graduate text Lectures on Modules and Rings, Springer GTM Vol. 189, 1999. Since that time, teaching obligations and intermittent intervention of other projects caused prolonged delays in the work on this volume. Only a lucky break in my schedule in 2006 enabled me to put the finishing touches on the completion of this long overdue book. This book is intended to serve a dual purpose. First, it is designed as a "problem book" for Lectures. As such, it contains the statements and full solutions of the many exercises that appeared in Lectures. Second, this book is also offered as a reference and repository for general information in the theory of modules and rings that may be hard to find in the standard textbooks in the field. As a companion volume to Lectures, this work covers the same math­ ematical material as its parent work; namely, the part of ring theory that makes substantial use of the notion of modules. The two books thus share the same table of contents, with the first half treating projective, injective, and flat modules, homological and uniform dimensions, and the second half dealing with noncommu
出版日期Book 2007
关键词Division; Volume; matrix
版次1
doihttps://doi.org/10.1007/978-0-387-48899-8
isbn_softcover978-1-4419-3175-7
isbn_ebook978-0-387-48899-8Series ISSN 0941-3502 Series E-ISSN 2197-8506
issn_series 0941-3502
copyrightSpringer-Verlag New York 2007
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Problem Books in Mathematicshttp://image.papertrans.cn/e/image/318520.jpg
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Post-WW2 Land Settlement in EuropeIn commutative algebra, localization of commutative rings . with respect to multiplicative sets . ⊆ . provides a powerful tool for proving theorems. For noncommutative rings, however, localization is a much more difficult proposition.
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Mesoamerican Political ComplexityWhile the classical right ring of quotients .(.) exists (if and) only if . is a right Ore ring, a . Q.(.) exists for any ring .. To define . (.), one must first understand the structure of the endomorphism ring of a QI (quasi-injective) module.
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From Legislation to Integration?A . (. QF) . is a ring . that is right injective and right (or equivalently, left) noetherian. Such a ring is always 2-sided artinian and 2-sided injective. In particular, “QF” is a left-right symmetric condition.
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Rings of Quotients,In commutative algebra, localization of commutative rings . with respect to multiplicative sets . ⊆ . provides a powerful tool for proving theorems. For noncommutative rings, however, localization is a much more difficult proposition.
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More Rings of Quotients,While the classical right ring of quotients .(.) exists (if and) only if . is a right Ore ring, a . Q.(.) exists for any ring .. To define . (.), one must first understand the structure of the endomorphism ring of a QI (quasi-injective) module.
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