Definition:Ring of Square Matrices

Definition
Let $R$ be a ring.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\map {\mathcal M_R} n$ denote the $n \times n$ matrix space over $R$.

Let $+$ denote the operation of matrix entrywise addition.

Let $\times$ be (temporarily) used to denote the operation of conventional matrix multiplication.

The algebraic structure:


 * $\struct {\map {\mathcal M_R} n, +, \times}$

is known as the ring of square matrices of order $n$ over $R$

Also see

 * Ring of Square Matrices over Ring is Ring
 * Ring of Square Matrices over Ring with Unity
 * Ring of Square Matrices over Field is Ring with Unity