As a continuation of the paper "Adjunction Identity to Hypersemigroup" in Turk J Math 2022; 46 (7): 2834--2853, it has been proved here that the adjunction of a greatest element to an ordered hypersemigroup is actually an embedding problem. The concept of pseudoideal has been introduced and has been proved that for each ordered hypersemigroup $S$ an ordered hypersemigroup $V$ having a greatest element ($poe$-hypersemigroup) can be constructed in such a way that there exists a pseudoideal $T$ of $S$ such that $S$ is isomorphic to $T$. If $S$ does not have a greatest element, then this can be regarded as the embedding of an ordered hypersemigroup in an ordered semigroup with greatest element.
$poe$-hypersemigroup, pseudoideal, embedding, semisimple, ideal, bi-ideal
"Adjunction greatest element to ordered hypersemigroups,"
Turkish Journal of Mathematics: Vol. 47:
6, Article 2.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss6/2