Free Ideal Rings and Localization in General Rings
by
P. M. Cohn
Book Details
Format
Hardback or Cased Book
Book Series
New Mathematical Monographs
ISBN-10
0521853370
ISBN-13
9780521853378
Publisher
Cambridge University Press
Imprint
Cambridge University Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 8th, 2006
Print length
594 Pages
Weight
961 grams
Dimensions
23.40 x 16.00 x 3.40 cms
Product Classification:
Algebra
Ksh 29,700.00
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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, and there is also a full account of localization. Each chapter has a number of exercises plus open problems and historical notes.
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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