On Ordered Regular Semigroups with a Zero Element

Abstract

In this paper, we study several conditions on ordered regular semigroups containing a zero element. In particular, we consider the natural and semigroup order and their connections to the properties of being principally ordered, Dubreil-Jacotin and BZS. We study also the set of biggest inverses in such a semigroup and we characterize subalgebras generated by two comparable idempotents.

Keywords

• ordered semigroups
• regular
• naturally ordered
• principally ordered
• strong dubreil-jacotin
• semilattice