Full Hypersubstitutions and Fully-solid Varieties of Semigroups

Abstract

In this paper we consider monoids of full hypersubstitutions and some of its submonoids. For the type τ = (2), that means, if there is only one binary operation symbol, we will determine all varieties of semigroups which are invariant under the application of all hypersubstitutions from these monoids. This gives complete sublattices of the lattice of all varieties of semigroups. We determine the greatest elements of such sublattices and prove that these varieties are finitely based by identities.