On Ordered Regular Semigroups with a Zero Element

Document Type : Original Scientific Paper


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


 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.


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