Abstract
For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component partsI,S o and Λ. The structure of images of this type of semigroups is also presented.
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