Abstract

For a variety V of algebras of type $ \tau $ , we consider the set M i (V) of all hypersubstitutions $ \sigma $ such that the variable x i is essential in the term $ \sigma $ (f) with respect to the variety V. We will give a complete answer to the question for which varieties V of type $ \tau $ = (n) the set M i (v) of hypersubstitutions forms a monoid. This is important since to every monoid of hypersubstitutions there corresponds a complete sublattice of the lattice of all varieties of algebras of the given type. For varieties of semigroups we get the monoid of all leftmost and all rightmost hypersubstitutions.

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