On Ordered Regular Semigroups with a Zero Element

نویسندگان

1 Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman

doi
10.22052/mir.2022.243017.1301
چکیده

 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.