On the Cayley semigroup of a finite aperiodic semigroup

Avi Mintz

Let $S$ be a finite semigroup. In this paper we introduce the functions ${\varphi }_s:S^{\ast }\to S^{\ast }$, first defined by Rhodes, given by $ϕ_s([a_1,a_2 ,...,a_n]) = [sa_1,sa_1a_2,..., sa_1a_2 .…