Abstract
A semigroup S is called E-inversive if for any a∈S there exists x∈S such that ax∈E(S). In this paper, the regular congruences on an E-inversive semigroup are investigated. It is proved that each regular congruence ρ on an E-inversive semigroup S is uniquely determined by the pair (ker ρ,tr ρ) and an abstract characterization of regular congruence ρ by means of the pair (ker ρ,tr ρ) (called regular congruence pair) is given. Also it is shown that each regular congruence on S is uniquely determined by its kernel normal system and a description of the regular congruences on S in terms of their kernel normal systems is given.
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