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COMPLETE LATTICE HOMOMORPHISM OF STRONGLY REGULAR CONGRUENCES ON $E$-INVERSIVE SEMIGROUPS

Part of: Semigroups Algebraic structures

Published online by Cambridge University Press:  28 October 2015

XINGKUI FAN ,
QIANHUA CHEN  and
XIANGJUN KONG
XINGKUI FAN*
Affiliation:
School of Science, Qingdao University of Technology, Qingdao, Shandong 266520, PR China email [email protected]
QIANHUA CHEN
Affiliation:
School of Science, Qingdao University of Technology, Qingdao, Shandong 266520, PR China email [email protected]
XIANGJUN KONG
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, PR China email [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

E-inversive semigroupsstrongly regular congruenceleft tracecomplete lattice homomorphismstrongly regular congruence triple

MSC classification

Primary: 20M10: General structure theory
Secondary: 08A30: Subalgebras, congruence relations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 100 , Issue 2 , April 2016 , pp. 199 - 215
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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