Eventually pointed principally ordered regular semigroups

الملخص EN

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 .