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Algebras of cancellative semigroups
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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