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COMPLETE LATTICE HOMOMORPHISM OF STRONGLY REGULAR CONGRUENCES ON
$E$-INVERSIVE SEMIGROUPS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 100 / Issue 2 / April 2016
- Published online by Cambridge University Press:
- 28 October 2015, pp. 199-215
- Print publication:
- April 2016
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- Article
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In this paper, we investigate strongly regular congruences on
$E$-inversive semigroups 
$S$. We describe the complete lattice homomorphism of strongly regular congruences, which is a generalization of an open problem of Pastijn and Petrich for regular semigroups. An abstract characterization of left and right traces for strongly regular congruences is given. The strongly regular (sr) congruences on 
$E$-inversive semigroups 
$S$ are described by means of certain strongly regular congruence triples 
$({\it\gamma},K,{\it\delta})$ consisting of certain sr-normal equivalences 
${\it\gamma}$ and 
${\it\delta}$ on 
$E(S)$ and a certain sr-normal subset 
$K$ of 
$S$. Further, we prove that each strongly regular congruence on 
$E$-inversive semigroups 
$S$ is uniquely determined by its associated strongly regular congruence triple.
