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Congruences contained in an equivalence on a semigroup

Part of: Algebraic structures Semigroups

Published online by Cambridge University Press:  09 April 2009

P. R. Jones
P. R. Jones
Affiliation:
Mathematics Department University of Western AustraliaNedlands, Western Australia 6009, Australia
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Abstract

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The main theorem of this paper shows that the lattice of congruences contained is some equivalence π on a semigroup S can be decomposed into a subdirect product of sublattices of the congruence lattices on the ‘prinipal π-facotrsρ of S—the semigroups formed by adjoining zeroes to the π-classes—whenever these are well-defined. The theorem is then applied to various equavalences and classes of semigroups to give some new results and alternative proofs of known ones.

MSC classification

Secondary: 20M10: General structure theory 08A30: Subalgebras, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 2 , March 1980 , pp. 162 - 176
Copyright
Copyright © Australian Mathematical Society 1980

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