Let "R" be a ring (not necessarily commutative). The set of all square matrices of size "n" with entries in "R" forms a ring with the entry-wise addition and the usual matrix multiplication. It is called the matrix ring and is denoted by M"n"("R"). Given a right "R"-module formula_140, the set of all "R"-linear maps from "U" to itself forms a ring with addition that is of function and multiplication that is of composition of functions; it is called the endomorphism ring of "U" and is denoted by formula_141.