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Universal fields of fractions for polycyclic group algebras

Published online by Cambridge University Press:  18 May 2009

D. S. Passman
D. S. Passman
Affiliation:
University of Wisconsin-Madison, Madison, Wisconsin 53706
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Let G be a polycyclic-by-finite group and let K[G] denote its group algebra over the field K. In this paper we discuss localization in K[G] and in particular we prove that every faithful completely prime ideal is localizable. Furthermore, using a sequence of localizations, we show that, for G polyinfinite cyclic, the classical right quotient ring (K[G]) is in fact a universal field of fractions for K[G]. Finally we offer an example of a domain K[G] which does not have a universal field of fractions.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 2 , July 1982 , pp. 103 - 113
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

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