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Algebras of cancellative semigroups

Published online by Cambridge University Press:  17 April 2009

Jan Okninski
Jan Okninski
Affiliation:
Institute of Mathematics, Warsaw University, Banacha 2, 02-791 Warsaw, Poland
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Abstract

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The Jacobson radical J(K[S]) of the semigroup ring K[S] of a cancellative semigroup S over a field K is studied. We show that, if J(K[S]) ≠ 0, then either S is a reversive semigroup or K[S] has many nilpotents and J(K[P]) ≠ 0 for a reversive subsemigroup P of S. This is used to prove that J(K[S]) = 0 for every unique product. semigroup S.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 1 , February 1994 , pp. 165 - 170
Copyright
Copyright © Australian Mathematical Society 1994

References

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