Free Ideal Rings and Localization in General Rings

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. There is also a full account of localization which is treated for general rings but the features arising in firs are given special attention.

Author: P. M. Cohn
Publisher: Cambridge University Press
Published: 06/08/2006
Pages: 594
Binding Type: Hardcover
Weight: 2.10lbs
Size: 9.00h x 6.00w x 1.40d
ISBN: 9780521853378

About the Author
Cohn, P. M.: - Paul Cohn is a Emeritus Professor of Mathematics at the University of London and Honorary Research Fellow at University College London.