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Localization in non-Noetherian group rings

Published online by Cambridge University Press:  18 May 2009

P. F. Smith
P. F. Smith
Affiliation:
Department of Mathematics, University Gardens, Glasgow G12 8QW
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Let k be a field and G an Abelian group of finite torsion-free rank. Brewer, Costa and Lady [1, Theorem A] showed that if k has characteristic 0 then each localization of the group algebra kG at a prime ideal is a regular local ring. They also showed (in the same theorem) that if k has characteristic p > 0, then kG is locally Noetherian (i.e. each localization of kG at a prime ideal is a Noetherian ring) if and only if G is an extension of a finitely generated group by a torsion p′-group. The purpose of this note is to examine this theorem in a more general setting.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 2 , July 1980 , pp. 151 - 163
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

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