Definition:Ring of Linear Operators

Theorem
Let $\mathcal L_R \left({G}\right)$ 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 $\left({\mathcal L_R \left({G}\right), +, \circ}\right)$ 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 $\left({G, +}\right)$.