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On semigroup algebras of cancellative commutative semigroups

Published online by Cambridge University Press:  14 November 2011

A. V. Kelarev
A. V. Kelarev
Affiliation:
Department of Mathematics and Mechanics, Ural State University, Lenina 51, Sverdlovsk 620083, U.S.S.R
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Synopsis

A cancellative commutative semigroup s and a hereditary radical ρ are constructed such that ρ is S-homogeneous but not S-normal. This answers a question which arose in the literature.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 1 - 3
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, vol 1, Mathematical Surveys 7 (Providence, R. I.: American Mathematical Society, 1961).Google Scholar
2Divinsky, N. J.. Rings and radicals (Toronto: Allen and Unwin, 1965).Google Scholar
3Jespers, E.. The Jacobson radical of semigroup rings of commutative semigroups. J. Algebra 109 (1987), 266–280.CrossRefGoogle Scholar
4Jespers, E. and Puczulowski, E. R.. The Jacobson radical of semigroup rings of commutative and cancellative semigroups. Comm. Algebra 12 (1984), 1115–1123.CrossRefGoogle Scholar
5Jespers, E., Krempa, J. and Wauters, P.. The Brown-McCoy radical of semigroup rings of commutative and cancellative semigroups. Glasgow Math. J. 26 (1985), 107–113.CrossRefGoogle Scholar
6Jespers, E. and Wauters, P.. A description of the Jacobson radical of semigroup rings of commutative semigroups. In Group and Semigroup Rings, ed. Karpilovski, G., 43–89 (Amsterdam: North Holland, 1986).Google Scholar
7Krempa, J.. Radicals of semigroup rings. Fund. Math. 85 (1974), 54–71.CrossRefGoogle Scholar
8Munn, W. D.. On commutative semigroup algebras. Math. Proc. Cambridge Philos. Soc. 93 (1983), 237–246.CrossRefGoogle Scholar
9Munn, W. D.. The algebra of a commutative semigroup over a commutative ring with unity. Proc. Roy. Soc. Edinburgh Sect. A 99 (1985), 387–398.CrossRefGoogle Scholar
10Okninski, J.. Radicals of group and semigroup rings. Contrib. Gen. Algebra 4 (1987), 125–150.Google Scholar
11Puczulowski, E. R.. Radicals of semigroup algebras of commutative and cancellative semigroups. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 317–323.CrossRefGoogle Scholar
12Wauters, P. and Jespers, E.. When is a semigroup ring of a commutative semigroup local or semilocal? J. Algebra 108 (1987), 188–194.CrossRefGoogle Scholar
13Wiegandt, R.. Radical and semisimple classes of rings (Kingston, Ontario: Queen's University, 1974).Google Scholar
14Kaarli, K., Okninski, J., Sands, A. D. and Veldsman, S.. Problems. Contrib. Gen. Algebra 4 (1987), 199–200.Google Scholar