Describing the Kernel of an identity-preserving ring morphism from a ring $R$ to an Endomorphism ring of an additive Abelian Group.

Question

I'm currently working through TS Blyth's book on Module Theory (Module Theory: An Approach to Linear Algebra). From Exercise 2.3:

"Let $M$ be an Abelian Additive Group, and $R$ a unitary ring. Let $\mu:R \to EndM $ be a ring morphism such that $\mu (1_R)=id_M$. Describe the kernel of this morphism."

What I know: The kernel is (obviously) an ideal. Also I know that $M$ is an $R$-module and that $M$ is an $EndM$-module (both from previous exercises). I haven't yet been able to work out exactly what this textbook assumes the reader knows, and I wouldn't be completely surprised if the question meant for me to explicitly prove that $kerM$ is a two-sided ideal. Is there any more information to be gathered about this morphism and its kernel from the assumptions? Thanks in advance for any hints.

Answer 1

I assume what they mean is that this homomorphism makes $M$ into an $R$-module and the kernel is the annihilator of $M$ over $R$.