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The radical of the algebra of any finite semigroup over any field

Published online by Cambridge University Press:  09 April 2009

T. E. Hall
T. E. Hall
Affiliation:
Monash UniversityClayton
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For a finite semigroup S and a field Φ, denote by Φ [S] the semigroup algebra of S over Φ and when S has a zero element, denote by Φ0[S] the contracted semigroup algebra of S over Φ (see § 5.2 [1]). Then theorem 5.31 [1], due to E.Hewitt and H. S. Zuckerman, gives a determination of the radical of Φ0[S] when S is commutative and the characteristic of Φ does not divide the order of any subgroup of S; and on page 168 [1] some results concerning the radical of Φ0[S] when S is completely 0-simple are given, the determination of the radical in the general case remaining open.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 350 - 352
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups (Math. Surveys, number 7, Amer. Math. Soc., Vol I, 1961).Google Scholar
[2]Lallement, G. and Petrich, M., ‘Irreducible matrix representations of finite semigroups’, Trans. Amer. Math. Soc. 139 (1969), 393–412.Google Scholar