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Lattice isomorphisms of orthodox semigroups

Published online by Cambridge University Press:  17 April 2009

Katherine G. Johnston  and
F.D. Cleary
Katherine G. Johnston
Affiliation:
Department of MathematicsRoyal Melbourne Institute of TechnologyP.O. Box 2476V Melbourne, Vic. 3001, Australia
F.D. Cleary
Affiliation:
Department of MathematicsRoyal Melbourne Institute of TechnologyP.O. Box 2476V Melbourne, Vic. 3001, Australia
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Abstract

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It is shown that the set of all orthodox subsemigroups of an orthodox semigroup forms a lattice. This lattice is a join-sublattice of the lattice of all semigroups, but is not in general a meet-sublattice. We obtain results concerning lattice isomorphisms between orthodox semigroups, several of which include known results for inverse semigroups as special cases.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 201 - 213
Copyright
Copyright © Australian Mathematical Society 1992

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