On right congruences of semigroups having no proper essential right congruences

A right congruence ?? in a semigroup S is essential if for any right congruence ?? we have ??????=?? (the identity relation) implies ??=??. Clearly, the universal relation, ??, is an essential right congruence. We say ?? is proper if ??????. 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.