Free Ideal Rings and Localization in General Rings 2024 pdf epub mobi 电子书

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发表于2024-09-27

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出版者:Cambridge Univ Pr

作者:Cohn, P. M.

出品人:

页数:594

译者:

出版时间:2006-6

价格:$ 255.38

装帧:HRD

isbn号码:9780521853378

丛书系列:New Mathematical Monographs

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Free Ideal Rings and Localization in General Rings 2024 pdf epub mobi 电子书图书描述

Proving that a polynomial ring in one variable over a field is a principal ideal domain can be done by means of the Euclidean algorithm, but this does not extend to more variables. However, if the variables are not allowed to commute, giving a free associative algebra, then there is a generalization, the weak algorithm, which can be used to prove that all one-sided ideals are free. This book presents the theory of free ideal rings (firs) in detail. Particular emphasis is placed on rings with a weak algorithm, exemplified by free associative algebras. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention. Each section has a number of exercises, including some open problems, and each chapter ends in a historical note.

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