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 ...
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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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Very Good. Cambridge: Cambridge University Press, 2006. Very Good. Cambridge: Cambridge University Press, 2006. Hard cover. 4. Very good. No dust jacket. 594 p. New Mathematical Monographs. Audience: Professional and scholarly. ORIGINAL hardcover; has minor shelf wear; otherwise a tight bright unmarked copy in very good shape overall; in a good dust jacket; never read!
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New. Contains: Line drawings, Unspecified. New Mathematical Monographs . 38 b/w illus. 864 exercises. Intended for professional and scholarly audience.
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