Free Ideal Rings and Localization in General Rings (New Mathematical Monographs) by P. M. Cohn
Cambridge University Press | July 3, 2006 | English | ISBN: 0521853370 | 596 pages | PDF | 2 MB
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.