On the Cayley semigroup of a finite aperiodic semigroup

2008/08/25 by Avi I. Mintz, Mintz, Avi
Computer Science · Mathematics · #semigroups and automata theory #Mathematical Dynamics and Fractals #Cellular Automata and Applications

paper · pdf · doi:10.48550/arxiv.0808.3415

Abstract

Let S be a finite semigroup. In this paper we introduce the functions ϕ_s:S^* → S^*, first defined by Rhodes, given by ϕ_s([a₁,a₂ ,...,a_n]) = [sa₁,sa₁a₂,..., sa₁a₂ ... a_n]. We show that if S is a finite aperiodic semigroup, then the semigroup generated by the functions \ϕ_s\_{s ∈ S} is finite and aperiodic.

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