It is shown that some embedding problems on hypersemigroups are actually problems of adjunction. According to the theorem of this paper, for every hypersemigroup $S$ which does not have identity element, an hypersemigroup $T$ having identity element can be constructed in such a way that $S$ is an ideal of $T$. Moreover, if $S$ is regular, intra-regular, right (left) regular, right (left) quasi-regular or semisimple, then so is $T$. If $A$ is an ideal, subidempotent bi-ideal or quasi-ideal of $S$, then it is an ideal, bi-ideal, quasi-ideal of $T$ as well. Illustrative examples are given.
"Adjunction identity to hypersemigroups,"
Turkish Journal of Mathematics: Vol. 46:
7, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/18