poe
-semigroup -that is an ordered semigroup (:po -semigroup) having a greatest element - is a semilattice of simple semigroups if and only if it is a semilattice of simple poe -semigroups [3].
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Kehayopulu, N., Tsingelis, M. On Intra-regular Ordered Semigroups. Semigroup Forum 57, 138–141 (1998). https://doi.org/10.1007/PL00005962
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DOI: https://doi.org/10.1007/PL00005962