Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-28T14:34:34.686Z Has data issue: false hasContentIssue false

Radicals of semigroup rings of commutative semigroups

Published online by Cambridge University Press:  24 October 2008

J. Okniński
Affiliation:
University of Warsaw, Warsaw, Poland
P. Wauters
Affiliation:
Katholieke Universiteit Leuven, Leuven, Belgium

Extract

In this paper we determine radicals of semigroup rings R[S] where R is an associative, not necessarily commutative, ring and S is a commutative semigroup. We will restrict ourselves to the prime radical P, the Levitzki radical L and the Jacobson radical J. At the end we will also give a few comments on the Brown-McCoy radical U.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Amitsur, S. A.. Radicals of polynomial rings. Canad. J. Math. 3 (1956), 355361.CrossRefGoogle Scholar
[2]Bergman, G. M.. On Jacobson radicals of graded rings. (Unpublished note.)Google Scholar
[3]Clifford, A. H. and Preston, G. B.. The Algebraic Theory of Semigroups.. Math. Surveys 7, vol. I (American Mathematical Society, 1961).Google Scholar
[4]Cohen, M. and Montgomery, S.. Group graded rings, smash products and group actions. Trans. Amer. Math. Soc. 282 (1984), 237258.CrossRefGoogle Scholar
[5]Divinsky, N. J.. Rings and Radicals (George Allen & Unwin Ltd., 1965).Google Scholar
[6]Jespers, E., Krempa, J. and Puczylowski, E.. On radicals of graded rings. Comm. Algebra 10 (1982), 18491854.CrossRefGoogle Scholar
[7]Jespers, E. and Puczylowski, E.. The Jacobson radical of semigroup rings of commutative cancellative semigroups. Comm. Algebra 12 (1984), 11151123.CrossRefGoogle Scholar
[8]Jespers, E., Krempa, J. and Wauters, P.. The Brown-McCoy radical of semigroup rings of commutative cancellative semigroups. Glasgow Math. J. 26 (1985), 107113.CrossRefGoogle Scholar
[9]Krempa, J.. Logical connections between some open problems concerning nil rings. Fund. Math. 76 (1972), 121130.CrossRefGoogle Scholar
[10]Krempa, J.. Radicals of semigroup rings. Fund. Math. 85 (1974), 5771.CrossRefGoogle Scholar
[11]Munn, W. D.. On commutative semigroup algebras. Math. Proc. Cambridge Philos. Soc. 93 (1983), 237246.CrossRefGoogle Scholar
[12]Munn, W. D.. The algebra of a commutative semigroup over a commutative ring with unity. Proc. Roy. Soc. Edinburgh Sect. 1. (To appear.)Google Scholar
[13]Munn, W. D.. On the Jacobson radical of certain commutative semigroup algebras. Math. Proc. Cambridge Philos. Soc. 96 (1984), 1523.CrossRefGoogle Scholar
[14]Okinński, J.. On the radical of semigroup algebras satisfying polnomial identities. Math. Proc. Cambridge Philos. Soc. 99 (1986), 4550.CrossRefGoogle Scholar
[15]Parker, T. and Gilmer, R.. Nilpotent elements of commutative semigroup rings. Michigan Math. J. 22 (1975), 97108.Google Scholar
[16]Procesi, C.. Rings with Polynomial Identities (Marcel Dekker, 1973).Google Scholar
[17]Puczylowski, E. R.. Behaviour of radical properties of rings under some algebraic constructions. (To appear.)Google Scholar
[18]Teply, M. L., Turman, E. G. and Quesada, A.. On semisimple semigroup rings. Proc. Amer. Math. Soc. 79 (1980), 157163.CrossRefGoogle Scholar
[19]Weissglass, J.. Semigroup rings and semilattice sums of rings. Proc. Amer. Math. Soc. 39 (1973), 471478.CrossRefGoogle Scholar