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Free Ideal Rings and Localization in General Rings (New Mathematical Monographs) by P. M. Cohn

Posted By: Free butterfly
Free Ideal Rings and Localization in General Rings (New Mathematical Monographs) by P. M. Cohn

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.