Abstract
A semigroup S is called an eventually regular semigroup if for every a ∈ S, there exists a positive integer n such that anis regular. In this paper, the R-unipotent, inverse semigroup and group congruences on an eventually regular semigroup S are described by means of certain congruence pairs (ξ, K), where ξ is a normal congruence on the subsemigroup 〈E(S)〉 generated by E(S), and K is a normal subsemigroup of S.
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