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Semilocal semigroup rings

Published online by Cambridge University Press:  18 May 2009

Jan Okniński
Jan Okniński
Affiliation:
University of Warsaw, 00-901 Warsaw, Poland.
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Semilocal and related classes of group rings have been investigated by many authors (cf. [10]). In particular, the following results have been obtained.

Theorem A[4,10]. Let K be a field and G a group.

(i) If ch K = 0, then K[G] is semilocal if and only if G is finite.

(ii) If ch K = p>0 and G is locally finite, then K[G] is semilocal if and only if G contains a p-subgroup of finite index.

In the case of semigroup rings some stronger conditions have been studied. Munn examined the semisimple artinian situation [6]. Zelmanov showed that if K[G]is artinian then G must be finite [11].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 37 - 44
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

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