A construction of left equalizer simple medial semigroups

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