where + as in is addition in "A", and function composition is denoted from right to left. Therefore, associated to any abelian group, is a ring. Conversely, given any ring, , is an abelian group. Furthermore, for every "r" in "R", right (or left) multiplication by "r" gives rise to a morphism of , by right (or left) distributivity. Let . Consider those endomorphisms of "A", that "factor through" right (or left) multiplication of "R". In other words, let End"R"("A") be the set of all morphisms "m" of "A", having the property that . It was seen that every "r" in "R" gives rise to a morphism of "A": right multiplication by "r". It is in fact true that this association of any element of "R", to a morphism of "A", as a function from "R" to End"R"("A"), is an isomorphism of rings. In this sense, therefore, any ring can be viewed as the endomorphism ring of some abelian "X"-group (by "X"-group, it is meant a group with "X" being its set of operators). In essence, the most general form of a ring, is the endomorphism group of some abelian "X"-group.