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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

REFERENCES

1.Cohn, P. M., Free rings and their relations (Academic Press, 1971).Google Scholar
2.Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, 1977).Google Scholar
3.Roseblade, J. E., Applications of the Artin-Rees lemma to group rings, Symposia Mathematica, 17 (1976), 471–478.Google Scholar
4.Roseblade, J. E., Prime ideals in group rings of polycyclic groups, Proc. London Math. Soc. (3) 36 (1978), 385–447.CrossRefGoogle Scholar
5.Roseblade, J. E. and Smith, P. F., A note on the Artin-Rees property of certain polycyclic group algebras, Bull. London Math. Soc. 11 (1979), 184–185.CrossRefGoogle Scholar
6.Smith, P. F., Localization and the AR property, Proc. London Math. Soc. (3) 22 (1971), 39–68.CrossRefGoogle Scholar
7.Smith, P. F., Localization in non-Noetherian group rings, Glasgow Math. J. 21 (1980), 151–163.CrossRefGoogle Scholar