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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