Abstract
A semigroup S is said to be left equalizer simple if, for all elements a, b, x, y of S, xa=xb implies ya=yb. 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 axyb=ayxb 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.
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