On the Cayley semigroup of a finite aperiodic semigroup

Avi Mintz

paper

On the Cayley semigroup of a finite aperiodic semigroup

arXiv:0808.3415

Abstract

Let $S$ be a finite semigroup. In this paper we introduce the functions $ϕ_{s} : S^{*} \to S^{*}$ , first defined by Rhodes, given by $ϕ_{s} ([a_{1}, a_{2}, ..., a_{n}]) = [s a_{1}, s a_{1} a_{2}, ..., s a_{1} a_{2} ... a_{n}]$ . We show that if $S$ is a finite aperiodic semigroup, then the semigroup generated by the functions ${ϕ_{s}}_{s \in S}$ is finite and aperiodic.