ALGEBRAS DERIVED BY SURJECTIVE HYPERSUBSTITUTIONS

Hypersubstitutions map operation symbols to terms of the corresponding arities. Using hypersubstitutions from each algebra one can derive new algebras. We compare properties of congruence lattices, of subalgebra lattices and of clones of the derived algebras with the corresponding properties of the starting algebras. If both algebras have the same clone of term operations, then they have the most properties in common. This is for instance the case if the hypersubstitution is surjective. We characterize surjective hypersubstitutions and prove that for finite types surjective hypersubstitutions are bijective. This will be applied to i-closed varieties of n-ary type.