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Semigroup Rings of Completely Regular Semigroups

In: Lattices, Semigroups, and Universal Algebra

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  • W. D. Munn

    (University of Glasgow, Department of Mathematics)

Abstract

A semigroup S is said to be completely regular if and only if it is covered by its subgroups; that is, if and only if, for each a ∈ S, a ∈ a2 S∩S a2. Groups and bands (semigroups of idempotents) are extreme special cases. In this paper a survey is given of results on the Jacobson radical of the semigroup ring of a completely regular semigroup over a ring with unity. Much of the inspiration is derived from the study of group rings, in which a similar interplay of two distinct branches of algebra is apparent. The work discussed covers a period of some thirty- six years, from the first paper on semigroup rings by Marianne Teissier (1952) to the present day.

Suggested Citation

  • W. D. Munn, 1990. "Semigroup Rings of Completely Regular Semigroups," Springer Books, in: Jorge Almeida & Gabriela Bordalo & Philip Dwinger (ed.), Lattices, Semigroups, and Universal Algebra, pages 191-201, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2608-1_21
    DOI: 10.1007/978-1-4899-2608-1_21
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