Algebras and clones III

On a set A, a collection of finitary functions which contains all projection maps and which is closed under composition is called a clone. This concept originated from logic, in particular, from the question which Boolean functions arise as compositions of a certain fixed set of Boolean functions. In Universal Algebra clones are studied since most properties of an algebraic structure actually depend on its clone of term functions rather than on the particular choice of its basic operations. First I will introduce the basic concepts of clone theory and its connections to algebra and computer science. Then I will give implicit descriptions of the polynomial functions on certain rings, groups, and more generally Mal'cev algebras.