On right inverse ordered semigroups

Abstract

A regular ordered semigroup S is called right inverse if every principal left ideal of S is generated by an R-unique positive element of it. We prove that a regular ordered semigroup is right inverse if and only if any two inverses of an element a ∈ S are R-related. Furthermore the class of right Clifford ordered semigroups have been characterized by the class of right inverse ordered semigroups.