Definition:Ring of Linear Operators

Theorem
Let $\map {\mathcal L_R} G$ be the set of all linear operators on $G$.

Let $\phi \circ \psi$ denote the composition of the two linear operators $\phi$ and $\psi$.

Then $\struct {\map {\mathcal L_R} G, +, \circ}$ 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 $\struct {G, +}$.