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On homogeneous radicals of semigroup rings of commutative semigroups

Published online by Cambridge University Press:  14 November 2011

A. V. Kelarev
Affiliation:
Department of Mathematics, University of Stellenbosch, 7600 Stellenbosch, South Africa

Synopsis

All Archimedean commutative semigroups S are described such that every S-homogeneous hereditary radical is S-normal. It is shown that this result is in a sense unimprovable.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1993

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References

1Auslander, M.. On regular group rings. Proc. Amer. Math. Soc. 8 (1957), 658664.CrossRefGoogle Scholar
2Brown, B. and McCoy, N. H.. The maximal regular ideal of a ring. Proc. Amer. Math. Soc. 1 (1950), 165171.CrossRefGoogle Scholar
3Gardner, B. J.. Radicals of Abelian groups and associative rings. Ada Math. Hungar. 24 (1973), 259268.CrossRefGoogle Scholar
4Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, Vol. 1, Math. Surveys 7 (Providence, R. I.: American Mathematical Society, 1961).Google Scholar
5Jespers, E.. When is the Jacobson radical of a semigroup ring of a commutative semigroup homogeneous? J. Algebra 109 (1987), 549560.CrossRefGoogle Scholar
6Jespers, E., Krempa, J. and Wauters, P.. The Brown-McCoy radical of semigroup rings of commutative and cancellative semigroups. Glasgow Math. J. 26 (1985), 107113.CrossRefGoogle Scholar
7Kaarli, K., Okninski, J., Sands, A. D. and Veldsman, S.. Problems. Contrib. Gen. Algebra 4 (1987), 199200.Google Scholar
8Kargapolov, M. I. and Mersljakov, Ju. J.. Fundamentals of the theory of groups (Berlin: Springer, 1979).CrossRefGoogle Scholar
9Kelarev, A. V.. Radicals and semigroup rings. Mat. Issledovaniya (Kishiniov) 105 (1988), 8192 (in Russian).Google Scholar
10Kelarev, A. V.. On the structure of the Jacobson radical of semigroup algebras of commutative semigroups. Issledovaniya Algebraich. System (Ekaterinburg) (1989), 7279 (in Russian).Google Scholar
11Kelarev, A. V.. When is the radical of a band sum of rings homogeneous? Comm. Algebra 18 (1990), 585603.CrossRefGoogle Scholar
12Kelarev, A. V.. On semigroup algebras of cancellative commutative semigroups. Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 13.CrossRefGoogle Scholar
13Munn, W. D.. The algebra of a commutative semigroup over a commutative ring with unity. Proc. Roy. Soc. Edinburgh Sect. A 99 (1985), 387398.CrossRefGoogle Scholar
14Okninski, J.. On regular semigroup rings. Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 145151.CrossRefGoogle Scholar
15Okninski, J.. Semigroup rings as excellent extensions and the regular radical. Simon Stevin 61 (1987), 301311.Google Scholar
16Puczylowski, E. R.. Radicals of semigroup algebras of commutative and cancellative semigroups. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 317323.CrossRefGoogle Scholar
17Puczylowski, E. R.. On unequivocal rings. Ada Math. Hungar. 36 (1988), 5762.CrossRefGoogle Scholar
18Weissglass, J.. Regularity of semigroup rings. Proc. Amer. Math. Soc. 25 (1970), 499503.CrossRefGoogle Scholar