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The regular radical of semigroup rings of commutative semigroups

Published online by Cambridge University Press:  18 May 2009

A. V. Kelarev
A. V. Kelarev
Affiliation:
Department of Mathematics and Mechanics, Ural State University, Lenina 51, Ekatherimburg 620083, Russia
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A description of regular group rings is well known (see [12]). Various authors have considered regular semigroup rings (see [17], [8], [10], [11], [4]). These rings have been characterized for many important classes of semigroups, although the general problem turns out to be rather difficult and still has not got a complete solution. It seems natural to describe the regular radical in semigroup rings for semigroups of the classes mentioned. In [10], the regular semigroup rings of commutative semigroups were described. The aim of the present paper is to characterize the regular radical ρ(R[S]) for each associative ring R and commutative semigroup S.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 133 - 141
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Vol. 1, Mathematical Surveys No. 7 (American Mathematical Society, 1961).Google Scholar
2.Goodearl, K. R., von Neumann regular rings (Pitman, 1979).Google Scholar
3.Jespers, E. and Wauters, P., A description of the Jacobson radical of semigroup rings of commutative semigroups, Group and semigroup rings, Proceedings of Conference, Johannesburg, 1985, Ed. Karpilovsky, G. (North-Holland, 1966), 43–89.Google Scholar
4.Kelarev, A. V., On regular semigroup rings, Semigroup Forum 40 (1990), 113–114.CrossRefGoogle Scholar
5.Kelarev, A. V., A description of the radicals of semigroup algebras of commutative semigroups, to appear.Google Scholar
6.Kelarev, A. V., On the Jacobson radical of semigroup rings of commutative semigroups, Math. Proc. Cambridge Philos. Soc. 108 (1990), 429–433.CrossRefGoogle Scholar
7.Krempa, J., Radicals of semigroup rings, Fund. Math. 85 (1974), 57–71.CrossRefGoogle Scholar
8.Munn, W. D., On the regularity of certain semigroup algebras, Semigroups, Proceedings of the Conference held at Monash University, 1979, Ed. Hall, T. E., Jones, P. R. and Preston, G. B. (Academic Press, 1980), 207–224.Google Scholar
9.Munn, W. D., On commutative semigroup algebras, Math. Proc. Cambridge Philos. Soc. 93 (1983), 237–246.CrossRefGoogle Scholar
10.Okniński, J., On regular semigroup rings, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 145–151.CrossRefGoogle Scholar
11.Okninski, J., Semigroup rings as excellent extensions and the regular radical, Simon Stevin 61 (1987), 301–311.Google Scholar
12.Passman, D. S., The algebraic structure of group rings (Wiley-Interscience, 1977).Google Scholar
13.Passman, D. S., Group rings, crossed products and Galois theory, CBMS Regional Conference Series in Mathematics, 64 (American Mathematical Society, 1986).Google Scholar
14.Ponizovskiî, I. S., An example of a semiprimitive semigroup algebra, Semigroup Forum 26 (1983), 225–228.CrossRefGoogle Scholar
15.Ponizovskiî, I. S., On semigroups rings, Semigroup Forum 28 (1984), 143–154.CrossRefGoogle Scholar
16.Teply, M. L., Turman, E. G. and Quesada, A., On semisimple semigroup rings, Proc. Amer. Math. Soc. 79 (1980), 157–163.CrossRefGoogle Scholar
17.Weissglass, J., Regularity of semigroup rings, Proc. Amer. Math. Soc. 25 (1970), 499–503.CrossRefGoogle Scholar