Simple generator modules Let a ring $R$ with identity element be such that the category of left $R$-modules has a simple generator $T$.
My question: "Is $T$ isomorphic with any simple left $R$-module $M$?"
I tried the meaning of generation by $T$, i.e. there exists an $R$-epimorphism $f$ from a direct sum $⊕T$ to $M$, but to no avail. Also, I know that any simple left $R$-module is isomorphic with $R/K$ for some maximal left ideal $K$ of $R$.  

Does this not just follow from the properties of semisimple modules?
If $S$ and $M$ are simple, and $(\oplus_{i\in I} S)/K\cong M$, then $M'\oplus K=(\oplus_{i\in I} S)$ where $M'\cong M$. So $M$ must be isomorphic to a direct sum of copies of $S$, but since it is simple it is just isomorphic to $S$.
