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On variants of a semigroup

Published online by Cambridge University Press:  17 April 2009

J. B. Hickey
J. B. Hickey
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW.
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Abstract

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If S is a (multiplicative) Semigroup and a ∈ S, the binary operation ∘ defined on the set S by x ∘ y = x a y is associative and the resulting semigroup is called a variant of S. We study the congruence a defined on S by saying that two elements are α-related if and only if they determine the same variant of S. Certain quotients of variants are used to provide an arbitrary semigroup with a generalised local structure. The variant formulation of Nambooripad's partial order on a regular semigroup is used to show that the order possesses a certain property (involving D-equivalence).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 447 - 459
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Blyth, T. S. and Hickey, J. B., “RP-dominated regular semigroups”, Proc. Roy. Soc. Edinburgh Sect. A 99 (1984), 185–191.Google Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, (vol. 1, Math. Surveys No. 7, Amer. Math. Soc. Providence, R.I., 1961).Google Scholar
[3]Green, D. G., “Extensions of a semilattice by an inverse semigroup”, Bull. Austral. Math. Soc. 9 (1973), 21–31.CrossRefGoogle Scholar
[4]Hickey, J. B., “Semigroups under a sandwich operation”, Proc. Edinburgh Math. Soc. 26 (1983), 371–382.Google Scholar
[5]Howie, J. M., An introduction to semigroup theory, (Academic Press, 1976).Google Scholar
[6]McAlister, D. B., “Regular Rees matrix semigroups and regular Debreil-Jacotin semigroups”, J. Austral. Math. Soc. (A) 31 (1981), 325–336.Google Scholar
[7]Magill, K. D. Jr., Misra, P. R. and Tewari, U. B., “Symons′ d-congruence on sandwich semigroups”, Czechoslovak Math. J. 33 (1983), 221–236.CrossRefGoogle Scholar
[8]Munn, W. D., “The idempotent-separating congruences on a regular 0-bisimple semigroup”, Proc. Edinburgh Math. Soc. (2) 15 (1967), 233–240.CrossRefGoogle Scholar
[9]Nambooripad, K. S. S., “The natural partial order on a regular semigroup”, Proc. Edinburgh Math. Soc. (2) 23 (1980), 249–260.CrossRefGoogle Scholar
[10]Symons, J. S. V., “On a generalization of the transformation semigroup”, J. Austral. Math. Soc. (A) 19 (1975), 47–61.Google Scholar