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The set of idempotents of a completely regular semigroup as a binary algebra

Published online by Cambridge University Press:  17 April 2009

Raymond Broeksteeg
Raymond Broeksteeg
Affiliation:
Mathematics DepartmentMonash University ClaytonVic 3168Australia e-mail: [email protected]
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Abstract

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A semigroup S is called E-solid if and only if for all idempotents e, f, g ∈ S such that e L f R g there exists an idempotent h ∈ S such that e R h L g. Each completely regular semigroup is E-solid. We characterise the idempotents of an arbitrary E-solid regular semigroup as a set with a binary operation on it satisfying a given finite set of identities.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 1 , August 1994 , pp. 91 - 107
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Broeksteeg, R., ‘The structure of solid binary algebras’, (preprint).Google Scholar
[2]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Math. Surveys No.7 (American Mathematical Society, Providence, R.I., 1961) (reprinted 1988).Google Scholar
[3]Easdown, D., ‘Biordered sets come from semigroups’, J. Algebra 96 (1985), 581–591.CrossRefGoogle Scholar
[4]Hall, T.E., ‘On regular semigroups’, J. Algebra 24 (1973), 1–24.CrossRefGoogle Scholar
[5]Higgins, P.M., Techniques of semigroup theory (Oxford University Press, 1992).CrossRefGoogle Scholar
[6]Howie, J.M., An introduction to semigroup theory, London Math. Soc. Monographs 7 (Academic Press, London, New York, 1976).Google Scholar
[7]Meakin, J., ‘Local semilattices on two generators’, Semigroup Forum 24 (1982), 95–116.CrossRefGoogle Scholar
[8]Meakin, J. and Pastijn, F., ‘The free pseudo-semilattice on two generators’, Algebra Universalis 14 (1982), 297–309.CrossRefGoogle Scholar
[9]Nambooripad, K.S.S., ‘Structure of regular semigroups I: Fundamental regular semigroups’, Semigroup Forum 9 (1975), 354–363.CrossRefGoogle Scholar
[10]Nambooripad, K.S.S., ‘Structure of regular semigroups I’, Mem. Amer. Math. Soc. 22 (1979 224).Google Scholar
[11]Nambooripad, K.S.S., ‘Pseudo-semilattices and biordered sets I’, Simon Stevin 55 (1981), 103–110.Google Scholar
[12]Yeh, Y.T., ‘The existence of e-free objects in e-varieties of regular semigroups’, Internat. J. Algebra Comput. 2 (1992), 471–484.CrossRefGoogle Scholar