An ordered semigroup S is said to be principally ordered if, for every x ∈ S there exists x* = max{y ∈ S | xyx ⩽ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1243,
author = {T.S. Blyth and G.A. Pinto},
title = {Pointed principally ordered regular semigroups},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {36},
year = {2016},
pages = {101-111},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1243}
}
T.S. Blyth; G.A. Pinto. Pointed principally ordered regular semigroups. Discussiones Mathematicae - General Algebra and Applications, Tome 36 (2016) pp. 101-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1243/
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