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 Composition of R-Algebraic Structure Homomorphisms, as it is a subring of the ring of all endomorphisms of the abelian group $$\left({G, +}\right)$$.