The algebraic closure of a function

Abstract: The algebraic operations on a set A which admit (as a homomorphism) a particular mapf∈A ^A, admit all powers off and certain other maps as well. The algebraic closure off, $$\bar f$$ , is the totality of all maps which admit the algebraic operations thatf does. The purpose of this paper is to characterize $$\bar f$$ in terms off, both forA finite and forA infinite.