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Congruence-free inverse semigroups with zero

Published online by Cambridge University Press:  09 April 2009

G. R. Baird
G. R. Baird
Affiliation:
University of Auckland, Auckland, New Zealand
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A semigroup is said to be congruence-free if it has only two congruences, the identity congruence and the universal congruence. It is almost immediate that a congruence-free semigroup of order greater than two must either be simple or 0-simple. In this paper we describe the semilattices of congruence-free inverse semi-groups with zero. Further, congruence-free inverse semigroups with zero are characterized in terms of partial isomorphisms of their semilattices. A general discussion of congruence-free inverse semigroups, with and without zero, is given by Munn (to appear).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 1 , August 1975 , pp. 110 - 114
Copyright
Copyright © Australian Mathematical Society 1975

References

Clifford, A. H., and Preston, G. B. (1961, 1967), The Algebraic Theory of Semigroups, Vol. I, Vol. II, Math. Surveys No. 7, Amer. Math. Soc., (Providence, R. I. 1961 and 1967.)Google Scholar
Lallement, G. (1966), ‘Congruences et équivalence de Green sur un demi-groupe régulier’, C. R. Acad. Sc. Paris, Série A 252, 613–616.Google Scholar
Munn, W. D. (1970), ‘Fundamental inverse semigroups’, Quart. J. Math., Oxford 21, 157–170.Google Scholar
Munn, W. D. (to appear), ‘Congruence-free inverse semigroups’, Quart. J. Math., Oxford.Google Scholar
Nivat, M. and Perrot, J.-F. (1970), ‘Une généralisation du monoide bicyclique’, C. R. Acad. Sci. Paris 271, 824–827.Google Scholar
Schein, B. M. (1966), ‘Homomorphisms and subdirect decompositions of semigroups’, Pacific J. Math. 17, 529–547.CrossRefGoogle Scholar