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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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