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The algebra of a commutative semigroup over a commutative ring with unity

Published online by Cambridge University Press:  14 November 2011

W. D. Munn
W. D. Munn
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
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Synopsis

A new description is provided for the nil radical of the algebra RS of a commutative semigroup S over a commutative ring R with a 1. It is shown that the Jacobson radical of RS is nil if the Jacobson radical of R is nil and that the converse holds in the case where S is periodic.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 387 - 398
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1Clifford, A. H. and Preston, G. B.. The algebraic theory of semigroups, Vol. I. Math. Surveys 7 (Providence, R.I.: Amer. Math. Soc, 1961).Google Scholar
2Connell, I. G.. On the group ring. Canad. J. Math. 15 (1963), 650–685.CrossRefGoogle Scholar
3Hewitt, E. and Zuckerman, H. S.. The l 1-algebra of a commutative semigroup. Trans. Amer. Math. Soc. 83 (1956), 70–97.Google Scholar
4Karpilovsky, G.. The Jacobson radical of commutative group rings. Arch. Math. 39 (1982), 428–430.CrossRefGoogle Scholar
5May, W., Group algebras over finitely generated rings. J. Algebra 39 (1976), 483–511.CrossRefGoogle Scholar
6Munn, W. D.. On commutative semigroup algebras. Math. Proc. Cambridge Philos. Soc. 93 (1983), 237–246.CrossRefGoogle Scholar
7Parker, T. and Gilmer, R.. Nilpotent elements of commutative semigroup rings. Michigan Math. J. 22 (1975–1976), 97–108.Google Scholar
8Preston, G. B.. Rédei's characterisation of congruences on finitely generated free commutative semigroups. Acta Math. Acad. Sci. Hungar. 26 (1975), 337–342.CrossRefGoogle Scholar
9Sierpińska, A.. K-completeness and its application to radicals of semigroup rings. Demonstratio Math. 13 (1980), 641–645.Google Scholar
10Zariski, O. and Samuel, P.. Commutative algebra Vol. I (Princeton, N.J.: Van Nostrand, 1958).Google Scholar