On ordered regular semigroups with biggest inverses (Q677097)

The authors consider only ordered regular semigroups \(S\) which have the property that every element \(x\) has a biggest inverse \(x^0\). The main result is: If \(e\), \(f\) are idempotents of \(S\) such that \(e\leq f\), then the semigroup \(\langle e,f,e^0,f^0\rangle\) is a principally ordered band with at most 24 elements. Also given is a complete description of this band and it is shown how it simplifies in natural special cases.