LEFT EQUALIZER SIMPLE SEMIGROUPS

We characterize and construct semigroups whose right regular representation is a left cancellative semigroup. These semigroups will be called left equalizer simple semigroups. For a congruence. on a semigroup S, let F[rho] denote the ideal of the semigroup algebra F[S] which determines the kernel of the extended homomorphism of F[S] onto F[S/rho] induced by the canonical homomorphism of S onto S/rho. We examine the right colons (F[rho] :(r) F[S]) = {a is an element of F[S] : F[S]a subset of F[rho]} in general, and in that special case when. has the property that the factor semigroup S/rho is left equalizer simple.