Theory of colored hypersubstitutions
by
Jörg Koppitz

A Hypersubstitution is a mapping from the set of all operation symbols of a given type in the set of all terms of this type wich preserves the arity. The set of all hypersubstitutions is denoted by Hyp. A multihypersubstitution is a mapping from the set of the natural numbers into the set Hyp. To apply a multihypersubstitution to a term we give in all terms each operation symbols a color (natural numbers). If we apply a multihypersubstitution m to a term we apply on the operation symbol with the color k the hypersubstitution m(k). Let V be a variety V of the given type. If we get by the application of the identities of V by the multihypersubstitutions again identities of V we say V is colored solid. In our talk we want to give the theory of the colored solid varieties like that for solid varieties. Further, we will give some examples for colored solid varieties of semigroups.

Date received: December 20, 2001