On ordered semigroups which are semilattices of left simple semigroups (Q2843881)

It is known that a semigroup \(S\) is a semilattice of left simple semigroups, i.e., it is decomposable into left simple semigroups if and only if \(S\) is left regular and every left ideal of \(S\) is two-sided. Moreover, this type of semigroups are the semigroups in which the set of left ideals is a semilattice under multiplication of subsets. In this paper, the authors deal with the possibility to extend such problems (and some analogous) results to the case of ordered semigroups.