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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

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