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Regular semigroups, fundamental semigroups and groups

  • D. B. McAlister (a1)

Abstract

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: ST between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

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References

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Byleen, K., Meakin, J. and Pastijn, F. (1978), ‘The fundamental 4-spiral semigroup’, J. Algebra 54, 626.
Clifford, A. H. and Preston, G. B. (1961), The algebraic theory of semigroups (Math. Surveys 7, Amer. Math. Soc., Providence, R.I.).
Fitz-Gerald, D. G. (1972), ‘On the inverses of products of idempotents in inverse semigroups’, J. Austral. Math. Soc. 13, 335337.
Grillet, P. A. (1974), ‘The structure of regular semigroups, I’, Semigroup Forum 8, 177187.
Hall, T. E. (1969), ‘On regular semigroups whose idempotents form a subsemigroup’, Bull. Austral. Math. Soc. 1, 195208.
Hall, T. E. (1972), ‘Congruences and Green's relations on regular semigroups’, Glasgow Math. J. 13, 167175.
Hall, T. E. (1973), ‘On regular semigroups’, J. Algebra 24, 124.
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press, London).
McAlister, D. B. (1974), ‘Groups, semilattices and inverse semigroups’, Trans. Amer. Math. Soc. 192, 227244.
McAlister, D. B. (1976), ‘ν-Prehomomorphisms on inverse semigroups’, Pacific J. Math. 67, 215231.
McAlister, D. B. (1980), ‘On a question of M. P. Schützenberger'’, Proc. Edinburgh Math. Soc. (to appear).
McAlister, D. B. and Reilly, N. R. (1977), ‘E-unitary covers for inverse semigroups’, Pacific J. Math. 68, 161174.
Munn, W. D. (1970), ‘Fundamental inverse semigroups’, Q. J. Math. Oxford Ser. 21, 157170.
Nambooripad, K. S. S. (1979), ‘The structure of regular semigroups, I’, Mem. Amer. Math. Soc. 224.
Nambooripad, K. S. S. (1980), ‘The natural partial order on a regular semigroup’ (submitted).
Rhodes, J. (1966), ‘Some results on finite semigroups’, J. Algebra 4, 471504.
Schein, B. M. (1966), ‘Semigroups of strong subsets’ (Russian), Volž. Mat. Sb. 4, 180186.
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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