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Regular semigroups, fundamental semigroups and groups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

D. B. McAlister
D. B. McAlister
Affiliation:
Department of Mathematical Sciences Northern Illinois UniversityDe Kalb, Illinois 60115, U.S.A.
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Abstract

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In this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 475 - 503
Copyright
Copyright © Australian Mathematical Society 1980

References

Byleen, K., Meakin, J. and Pastijn, F. (1978), ‘The fundamental 4-spiral semigroup’, J. Algebra 54, 6–26.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B. (1961), The algebraic theory of semigroups (Math. Surveys 7, Amer. Math. Soc., Providence, R.I.).Google Scholar
Fitz-Gerald, D. G. (1972), ‘On the inverses of products of idempotents in inverse semigroups’, J. Austral. Math. Soc. 13, 335–337.CrossRefGoogle Scholar
Grillet, P. A. (1974), ‘The structure of regular semigroups, I’, Semigroup Forum 8, 177–187.CrossRefGoogle Scholar
Hall, T. E. (1969), ‘On regular semigroups whose idempotents form a subsemigroup’, Bull. Austral. Math. Soc. 1, 195–208.CrossRefGoogle Scholar
Hall, T. E. (1972), ‘Congruences and Green's relations on regular semigroups’, Glasgow Math. J. 13, 167–175.CrossRefGoogle Scholar
Hall, T. E. (1973), ‘On regular semigroups’, J. Algebra 24, 1–24.CrossRefGoogle Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).Google Scholar
McAlister, D. B. (1974), ‘Groups, semilattices and inverse semigroups’, Trans. Amer. Math. Soc. 192, 227–244.Google Scholar
McAlister, D. B. (1976), ‘ν-Prehomomorphisms on inverse semigroups’, Pacific J. Math. 67, 215–231.CrossRefGoogle Scholar
McAlister, D. B. (1980), ‘On a question of M. P. Schützenberger'’, Proc. Edinburgh Math. Soc. (to appear).CrossRefGoogle Scholar
McAlister, D. B. and Reilly, N. R. (1977), ‘E-unitary covers for inverse semigroups’, Pacific J. Math. 68, 161–174.CrossRefGoogle Scholar
Munn, W. D. (1970), ‘Fundamental inverse semigroups’, Q. J. Math. Oxford Ser. 21, 157–170.CrossRefGoogle Scholar
Nambooripad, K. S. S. (1979), ‘The structure of regular semigroups, I’, Mem. Amer. Math. Soc. 224.Google Scholar
Nambooripad, K. S. S. (1980), ‘The natural partial order on a regular semigroup’ (submitted).CrossRefGoogle Scholar
Rhodes, J. (1966), ‘Some results on finite semigroups’, J. Algebra 4, 471–504.CrossRefGoogle Scholar
Schein, B. M. (1966), ‘Semigroups of strong subsets’ (Russian), Volž. Mat. Sb. 4, 180–186.Google Scholar