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Free Ideal Rings and Localization in General Rings
P. M. Cohn
出版Cambridge University Press, 2006-06-08
主題Mathematics / Algebra / General
ISBN11394549949781139454995
URLhttp://books.google.com.hk/books?id=YLnF1CE4xDUC&hl=&source=gbs_api
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註釋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.