Abstract
A right congruence ρ in a semigroup S is essential if for any right congruence σ we have ρ∧σ=ι (the identity relation) implies σ=ι. Clearly, the universal relation, ν, is an essential right congruence. We say ρ is proper if ρ≠ν. In this paper we get a necessary and sufficient condition for a semigroup with an identity element 1 and having no proper essential right congruences to have a distributive lattice of right congruences.
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