Extensions of Congruences on Subsemingroups of Semigroups

Abstract:

      Let ρ be a congruence on a semingroup S.ρis called a rectangular band congruence if S/ρ is a rectangular band. In this paper the least restangular band congruence on a senigroup is disccribed . Let T be a subsemigroup of a semigroup S. A necessary and sufficient condition for which every rectangular band congruence on T can be uniquely extended to a rectangular band congruence on S is given.