Colored Solid Varieties of Semigroups
by
Joerg Koppitz
University of Potsdam, Germany

A hypersubstitution of type \tau is a mapping from the set of the operation symbols in the set of all terms of type \tau, which preserves the arity. We want to consider so-called colored hypersubstitutions. For this we give the set of terms a coloration by marking the operation symbols in all term by natural numbers. A colored hypersubstitution is a mapping from the set of all natural numbers in the set of all hypersubstitutions of type \tau. If we apply a colored hypersubstitution of type \tau to a term of type \tau we apply of each one of the operation symbols the hypersubstitution which is the image of its color. So, one can in a given term apply on the same operation symbol different hypersubstitutions if it occurs on different places.

Similar to solid varieties of type \tau we can define colored-solid varieties of type \tau. We will describe colored-solid varieties of semigroups.

Date received: July 13, 2001