Some Remarks on Paramedial Semigroups and Medial Semigroups

Nares Sawatraksa, Chaiwat Namnak, Chaiwat Namnak

Abstract

Let S be a semigroup. We say that S is a medial if abcd = acbdfor all a,b,c,d ∈ S and S is a paramedial if abcd = dbca for all a,b,c,d ∈ S. In this paper, we investigate some properties of the regularity and Green's relations. Moreover, we describe compatibility with the natural partial order on paramedial semigroups and medial semigroups.