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.
Buy Free Ideal Rings and Localization in General Rings book by P. M. Cohn from Australia's Online Bookstore, Boomerang Books.
(228mm x 152mm x 34mm)
Cambridge University Press
Publisher: Cambridge University Press
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Author Biography - P. M. Cohn
Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.