| Abstract: | 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 \({\varrho}\) on a semigroup S, let \({{\mathbb F}\varrho]}\) denote the ideal of the semigroup algebra \({{\mathbb F}S]}\) which determines the kernel of the extended homomorphism of \({{\mathbb F}S]}\) onto \({{\mathbb F}S/\varrho]}\) induced by the canonical homomorphism of S onto \({S/\varrho}\). We examine the right colons (\({{\mathbb F}\varrho] :_{r} {\mathbb F}S]) = {a \epsilon {\mathbb F}S] : {\mathbb F}S]a \subseteqq {\mathbb F}\varrho]}}\) in general, and in that special case when \({\varrho}\) has the property that the factor semigroup \({S/\varrho}\) is left equalizer simple. |
