ENGLISH

Free Ideal Rings and Localization in General Rings

By P. M. Cohn

Book information

Publisher
Cambridge University Press
Year
2006
ISBN
0521853370, 9780521853378
Open Library ID
OL7766782M
Language
english
Format
PDF
Filesize
3 MB (2889294 bytes)
Series
New Mathematical Monographs
Pages
596\596
Time added
2011-01-06 10:13:16

Description

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.

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