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Titlebook: Noncommutative Algebra; Benson Farb,R. Keith Dennis Textbook 1993 Springer Science+Business Media New York 1993 K-theory.algebra.commutati

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樓主
發(fā)表于 2025-3-21 19:13:46 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Noncommutative Algebra
編輯Benson Farb,R. Keith Dennis
視頻videohttp://file.papertrans.cn/668/667186/667186.mp4
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Noncommutative Algebra;  Benson Farb,R. Keith Dennis Textbook 1993 Springer Science+Business Media New York 1993 K-theory.algebra.commutati
描述About This Book This book is meant to be used by beginning graduate students. It covers basic material needed by any student of algebra, and is essential to those specializing in ring theory, homological algebra, representation theory and K-theory, among others. It will also be of interest to students of algebraic topology, functional analysis, differential geometry and number theory. Our approach is more homological than ring-theoretic, as this leads the to many important areas of mathematics. This ap- student more quickly proach is also, we believe, cleaner and easier to understand. However, the more classical, ring-theoretic approach, as well as modern extensions, are also presented via several exercises and sections in Chapter Five. We have tried not to leave any gaps on the paths to proving the main theorem- at most we ask the reader to fill in details for some of the sideline results; indeed this can be a fruitful way of solidifying one‘s understanding.
出版日期Textbook 1993
關(guān)鍵詞K-theory; algebra; commutative algebra; commutative ring; representation theory
版次1
doihttps://doi.org/10.1007/978-1-4612-0889-1
isbn_softcover978-1-4612-6936-6
isbn_ebook978-1-4612-0889-1Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1993
The information of publication is updating

書目名稱Noncommutative Algebra影響因子(影響力)




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沙發(fā)
發(fā)表于 2025-3-21 22:19:10 | 只看該作者
Semisimple Modules & Rings and the Wedderburn Structure Theoremis to express that object in terms of simpler, better understood pieces. For example, the Wedderburn Structure Theorem says that any semisimple ring (we’ll define this later) is isomorphic to a finite product of matrix rings over division rings, each of which is simple. The theory for semisimple mod
板凳
發(fā)表于 2025-3-22 00:52:38 | 只看該作者
地板
發(fā)表于 2025-3-22 05:56:57 | 只看該作者
The Brauer Groups Theorem shows that . and . are the only finite dimensional central division algebras over .. This kind of classification is optimal in the sense that we have an explicit, easy-to-understand list of all finite dimensional central division algebras over .. Classifying finite dimensional central divi
5#
發(fā)表于 2025-3-22 10:33:32 | 只看該作者
6#
發(fā)表于 2025-3-22 15:17:12 | 只看該作者
Burnside’s Theorem and Representations of Finite Groupsation theory of finite groups is a vast subject; in this chapter we’ll make a thin beeline right to a famous theorem of Burnside. For a more thorough introduction to the representation theory of finite groups, the reader may consult Serre, ., as well as Fulton and Harris, ..
7#
發(fā)表于 2025-3-22 17:29:02 | 只看該作者
The Global Dimension of a Ringn Chapters 1 and 2 can be considered the zero’th step in the theory of global dimension. Kaplansky, based upon an observation of Schanuel, was the first to set down the dimension theory of rings in an elementary way, without using the powerful machinery of homological algebra. This section is based
8#
發(fā)表于 2025-3-22 23:43:15 | 只看該作者
The Brauer Group of a Commutative Ringroup coincides with the “classical” Brauer group (cf. Chapter 4) in the case when . is a field. One of the points of extending the theory to rings is that one can relate Brauer groups of fields to Brauer groups of related rings in exact sequences; one then hopes that this will help compute the class
9#
發(fā)表于 2025-3-23 02:17:15 | 只看該作者
Benson Farb,R. Keith Dennisahren das Bestreben besteht, z. B. den Wirkungsgrad der dampftechnischen und elektrischen Anlagen auf das h?chstm?gliche Ma? heraufzubringen, ist bis jetzt dem Wirkungsgrad der Anlagen in den Betrieben so gut wie keine Beachtung geschenkt worden. Es handelt sich hierbei um alle diejenigen industriel
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發(fā)表于 2025-3-23 09:04:08 | 只看該作者
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