Definition:Ring of Linear Operators

Definition
Let $R$ be a ring.

Let $G$ be an $R$-module.

Let $\map {\LL_R} G$ denote the set of all linear operators on $G$.

Let $+$ and $\circ$ be the binary operations on $\map {\LL_R} G$ defined such that:
 * $+$ denotes pointwise addition
 * $\circ$ denotes composition of linear operators.

Then the algebraic structure:
 * $\struct {\map {\LL_R} G, +, \circ}$ is a ring

is known as the ring of linear operators on $G$.

Also see

 * Ring of Linear Operators is Ring