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.
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© 1987 D. Reidel Publishing Company
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Munn, W.D. (1987). A Class of Inverse Semigroup Algebras. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_14
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DOI: https://doi.org/10.1007/978-94-009-3839-7_14
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