Show that a simple ring $R$ is always an algebra over some field.
So I need to show that there exist a field $k$ such that there exists a ring homomorphism $\phi : k \to Z(R) $.
In an earlier exercise I've proven that a simple commutative ring is a field.
Any hints how to tackle this problem ?
If $a$ is nonzero and in the center, then the two sided ideal $aR=R$. Thus, the center is a field.