Adjunction identity to hypersemigroups

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.