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On the radical of semigroup algebras satisfying polynomial identities

Published online by Cambridge University Press:  24 October 2008

Jan Okniński
Jan Okniński
Affiliation:
Institute of Mathematics, University of Warsaw, 00–901 Warsaw, Poland
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Extract

In this paper we will be concerned with the problem of describing the Jacobson radical of the semigroup algebra K[S] of an arbitrary semigroup S over a field K in the case where this algebra satisfies a polynomial identity. Recently, Munn characterized the radical of commutative semigroup algebras [9]. The key to his result was to show that, in this situation, the radical must be a nilideal. We are going to extend the latter to the case of PI-semigroup algebras. Further, we characterize the radical by means of the properties of S or, more precisely, by some groups derived from S. For this purpose we will exploit earlier results leading towards a characterization of semigroup algebras satisfying polynomial identities [5], [15], which generalized the well known case of group algebras (cf. [13], chap. 5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 45 - 50
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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