Eventually Pointed Principally Ordered Regular Semigroups

G.A. Pinto

Abstract


An ordered regular semigroup, , is said to be principally ordered if for every  there exists . A principally ordered regular semigroup is pointed if for every element,  we have . Here we investigate those principally ordered regular semigroups that are eventually pointed in the sense that for all  there exists a positive integer, , such that . Necessary and sufficient conditions for an eventually pointed principally ordered regular semigroup to be naturally ordered and to be completely simple are obtained. We describe the subalgebra of  generated by a pair of comparable idempotents  and such that .

 


Keywords


Regular semigroup; Strong Dubreil-Jacotin; Principally ordered; Naturally ordered; Pointed principally ordered; Green’s relations; Completely simple.

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References


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DOI: http://dx.doi.org/10.24200/squjs.vol24iss2pp139-146

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