A Class of Inverse Semigroup Algebras

W. D. Munn
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W. D. Munn: University of Glasgow, Department of Mathematics

A chapter in Semigroups and Their Applications, 1987, pp 111-119 from Springer

Abstract: Abstract In 1976, Domanov showed that the algebra of an inverse semigroup S over a field F is semiprimitive (that is, has zero Jacobson radical) if the algebra of each maximal subgroup of S over F is semiprimitive. It is known that the converse statement is false in general. The principal purpose of this paper is to announce that if the semi-lattice of S satisfies a certain finiteness condition, introduced by Teply, Turman and Quesada in 1980, then the converse does hold. Corresponding results for primitivity are also discussed.

Date: 1987
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DOI: 10.1007/978-94-009-3839-7_14

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