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Coextensions of pseudo-Inverse semigroups by rectangular bands

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

John Meakin
John Meakin
Affiliation:
Department of Mathematics and Statistics, University of Nebraska, Lincoln, NE 68588, U.S.A. Department of Mathematics, University of Kerala, Kariavattom 695581, India
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Abstract

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We say that a regulär semigroup S is a coetension of a (regular) semigroup T by rectangular bands if there is a homomorphism ϕ: S → T from S onto T such that, for each e = e2 ∈ S, e(ϕ ϕ-1) is a rectangular band. Regular semigroups which are coextesions of pseudo-inverse semigroups by rectangular bands may be characterized as those regular semigroups S with the property that, for each e = e2 ∈ S, ω(e) = {f = f2 ∈ S: ef = f} and ωl(e) = {f = f2 ∈ S: fe = f} are bands: this paper is concerned with a study of such semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 30 , Issue 1 , September 1980 , pp. 73 - 86
Copyright
Copyright © Australian Mathematical Society 1980

References

Byleen, K. (1977), The structure of regular and inverse semigroups (Ph.D. Thesis, University of Nebraska).Google Scholar
Byleen, K., Meakin, J. and Pastijn, F. (1980), ‘The double four-spiral semigroup’, Simon Stevin (to appear).Google Scholar
Clifford, A. H. and Preston, G. B. (1961), The algebraic theory of semigroups, Vol. I (Math. Surveys No. 7, Amer. Math. Soc.).Google Scholar
Hall, T. E. (1971), ‘Orthodox semigroups’, Pacific J. Math. 39, 677–686.CrossRefGoogle Scholar
Howie, J. M. (1976), An introduction to semigroup theory (Academic Press Inc.).Google Scholar
Lallement, G. (1967), ‘Demi-groupes régulieres’, Ann. Math. Pura Appl. 77, 47–129.CrossRefGoogle Scholar
Meakin, J. and Nambooripad, K. S. S. (1979a), ‘Coextension of regular semigroups by rectangular bands I’, preprint, University of Nebraska.Google Scholar
Meakin, J. and Nambooripad, K. S. S. (1979b), ‘Coextensions of regular semigroups by rectangular bands II’, preprint, University of Nebraska.Google Scholar
Nambooripad, K. S. S. (1979), Structure of regular semigroups I (Mem. Amer. Math. Soc. 224, Amer. Math. Soc., Providence, R.I.).CrossRefGoogle Scholar
Nambooripad, K. S. S. (1978), ‘Pseudo-semilattices and biordered sets’, preprint, University of Kerala.Google Scholar
Nambooripad, K. S. S. and Sitaraman, Y. (1979), ‘On some congruences on regular semigroups’, J. Algebra (to appear).CrossRefGoogle Scholar
Preston, G. B. (1958), ‘Matrix representations of semigroups’, Quart. J. Math Oxford Ser. 9, 169–176.CrossRefGoogle Scholar
Schein, B.M. (1972), ‘Pseudo-semilattices and pseudo-lattices’, Izv. Vyss. Ucebn. Zaved. Matematika 2 (117), 81–94 (in Russian).Google Scholar
Yamada, M. and Kimura, Y. (1958), ‘Note on idempotent semigroups II’, Proc. Japan Acad. 34, 110–112.Google Scholar