A construction of left equalizer simple medial semigroups

Abstract A semigroup S is said to be left equalizer simple if, for all elements a , b x y of $$xa=xb$$ x a = b implies $$ya=yb$$ y . It known that simplicity necessary condition embedded in semigroup. satisfying the identity $$axyb=ayxb$$ called medial In this paper we show how construct semigroups, especially, semigroups which can idempotent-free semigroups.