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

摘要

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 (gamma, K, delta) consisting of certain sr-normal equivalences gamma and 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.