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Semiprimitivity of inverse semigroup algebras

Published online by Cambridge University Press:  14 November 2011

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Synopsis

Let S be an inverse semigroup and F a field. It is shown that if F has characteristic 0 and is not algebraic over its prime subfield then the algebra of S over F is semiprimitive (i.e. Jacobson semisimple). This generalises a well-known theorem on group algebras due to Amitsur. Similar results for the case in which F has prime characteristic are obtained under the additional hypotheses that S is completely semisimple or that S is E-unitary with a totally ordered semilattice.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 1-2 , 1982 , pp. 83 - 98
Copyright
Copyright © Royal Society of Edinburgh 1982

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