Ring of Linear Operators is Ring

Theorem
Let $R$ be a ring.

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

Let $\struct {\map {\LL_R} G, +, \circ}$ be the ring of linear operators on $G$, where:
 * $+$ denotes pointwise addition
 * $\circ$ denotes composition of linear operators.

Then $\struct {\map {\LL_R} G, +, \circ}$ is a ring.

Proof
Follows from Composite of R-Algebraic Structure Homomorphisms is Homomorphism, as it is a subring of the ring of all endomorphisms of the abelian group $\struct {G, +}$.