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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

[1]Clifford, A.H. and Preston, G.B., Algebraic theory of semigroups, 1 (American Mathematical Society, Providence, RI, 1961).CrossRefGoogle Scholar
[2]Jespers, E., Krempa, J. and Puczylowski, E., ‘On radicals of graded rings’, Comm. Algebra 10 (17) (1982), 1849–1854.CrossRefGoogle Scholar
[3]Karpilovsky, G., The Jacobson radical of classical rings, Pitman Monographs and Surveys in Pure and Applied Mathematics (Longman, 1991).Google Scholar
[4]Okninski, J., Semigroup algebras, Monographs and Textbooks in Pure and Applied Mathematics 138 (Marcel Dekker, 1991).Google Scholar
[5]Okninski, J., ‘Prime and semiprime semigroup rings of cancellative semigroups’, Glasgow Math. J. 35 (1993), 1–12.CrossRefGoogle Scholar
[6]Passman, D.S., The algebraic structure of group rings (Wiley, New York, 1977).Google Scholar
[7]Passman, D.S., Infinite crossed products, Pure and Applied Mathematics 135 (Academic Press, New York, 1989).Google Scholar
[8]Strojnowski, A., ‘A note on u.p. groups’, Comm. Algebra 8 (1980), 231–234.CrossRefGoogle Scholar