Suppose you have two free modules $M$ and $N$ of finite rank over a commutative ring $R$. Let's also take some $f\in\operatorname{End}_R(M)$ and $g\in\operatorname{End}_R(N)$, which gives a corresponding $f\otimes g\in\operatorname{End}_R(M\otimes N)$.
Apparently, the trace of these endomorphisms "distributes" over the tensor product, in that $ \operatorname{tr}(f\otimes g)=\operatorname{tr}f\operatorname{tr}g. $
This is not clear to me. Is there an explanation why this is true?