HYPERIDENTITIES FOR SOME VARIETIES OF COMMUTATIVE SEMIGROUPS

Hyperidentities and hypervarieties have been defined by Taylor in [5]. A hypervariety is a class of varieties closed under the formation of equivalent, product, reduct and subvarieties. Hyperidentities are used to define hypervarieties, in the same way that ordinary identities define varieties. This paper produces some hyperidentities satisfied by various varieties of commutative semigroups, and identifies some restrictions as to what kind of hyperidentities such varieties can satisfy. It also continues the study, begun in [6], of the closure and hypervariety operators defined there, as they apply to varieties of commutative semigroups.