Associative nontrivial hyperidentities in semigroups

The paper gives a characterization of the class of semigroups in which the nontrivial associative hyperidentity is essentially satisfied. It is proved that, in difference to the case of trivial associative hyperidentity, the class of all semigroups, in which a nontrivial associative hyperidentity is essentially satisfied, is a finite union of finitely based varieties of semigroups, and the basis identities of all varieties are explicitly inscribed.