POINTED PRINCIPALLY ORDERED REGULAR SEMIGROUPS

Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2016, Vol 36, Issue 1

Abstract

An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x⋆ = max {y ∈ S | xyx 6 x}. Here we investigate those principally ordered regular semigroups that are pointed in the sense that the classes modulo Green’s relations L, R, D have biggest elements which are idempotent. Such a semigroup is necessarily a semiband. In particular we describe the subalgebra of (S;⋆) generated by a pair of comparable idempotents that are D-related. We also prove that those D-classes which are subsemigroups are ordered rectangular bands.

Authors and Affiliations

T. S. Blyth, G. A. Pinto

Keywords

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  • EP ID EP304505
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How To Cite

T. S. Blyth, G. A. Pinto (2016). POINTED PRINCIPALLY ORDERED REGULAR SEMIGROUPS. Discussiones Mathematicae - General Algebra and Applications, 36(1), -. https://europub.co.uk./articles/-A-304505