To help myself prepare for an upcoming exam, I've been working on various problems that focus on the topics we have been dealing with in class. I came across this one:
Let $M$ be a right $R$-module such that $M / Soc(M)$ is finitely generated. Show that $M = A \oplus B$, where $A_R$ is finitely generated, and $B_R$ is semisimple.
Any help would be greatly appreciated. Thanks!