In abstract algebra, a matrix ring is any collection of matrices over some ring R that form a ring under matrix addition and matrix multiplication . The set of n × n matrices with entries from R is a matrix ring denoted Mn(R), as well as some subsets of infinite matrices which form infinite matrix rings. Any subring of a matrix ring is a matrix ring. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra, and may be called a matrix algebra. For this case, if M is a matrix and r is in R, then the matrix Mr is the matrix M with each of its entries multiplied by r. This article assumes that R is an associative ring with a unit 1 ≠ 0, although matrix rings can be formed over rings without unity.