On algebras and clones
Clones of term functions are considered under the aspect of the structure of algebras. If A is an algebra, denote by T(A) the clone of term functions of A. The main topic is a mapping \(T: {\mathcal V}\to C\) from a class of algebras to the class of clones of term functions. It is shown that the class T(\({\mathcal V})\) is a \(\vee\)-sublattice of the lattice of subvarieties of the variety of clones. The clone equations are much easier to handle if they are given in the form of hyperidentities. By this method it is pointed out that the primal algebras give rise to an infinite chain of varieties in T(\({\mathcal V})\) and there are given hyperidentities for some varieties of lattices and abelian groups. For varieties in T(\({\mathcal V})\) there are found some subdirectly irreducible clones.
scientific article; zbMATH DE number 3993660