The entropy function on an algebraic structure with inflnite partition and m¡preserving transformation generators

One of the applied branches of mathematics is the entropy of a dynamical system. In this paper we deflned the inflnite partition of an algebraic structure and then we introduce the entropy of a countable partition of this structure. In this respect, we introduce the generators of an m-preserving transformation of a discrete dynamical system. At the end, we prove a version of Kolomogorov-Sinai theorem concerning the entropy of a dynamical system.