Abstract
Hyperidentities and hypervarieties have been defined by Taylor in [4]. A hypervariety is a class of varieties closed under the formation of equivalent, product, reduct and sub-varieties. Hyperidentities are used to define hypervarieties, in the same way that ordinary identities define varieties. In this paper we consider hyperidentities for hypervarieties generated by two types of varieties of semigroups, varieties of bands and varieties of nilpotent semigroups. We introduce two operators on the lattice of varieties of semigroups, the closure and hypervariety operators, and study their properties.
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