$V$ is a left $R$ module, how do you understand the ring homomorphism $$\rho_{V}:R \to End_Z(V)$$
I know that it is like a group acting on sets, but it is very easy to understand like a group $S_n$ act on set $X$ for permutation, so how can you understand $End_Z(V)$ under this scenario ?
And also since this has something to do with representation theory, so (if I understand correctly), $End_Z(V)$ can be think as all linear transformation, so what about the element of $R$ here ? Seems that I haven't build a bridge between rings and its effects on modules so far...