quality:correction
Theorem A (rings)

Let R {\displaystyle R} and S {\displaystyle S} be rings, and let φ: R → S {\displaystyle \varphi:R\rightarrow S} be a ring homomorphism. Then:

In particular, if φ {\displaystyle \varphi } is surjective then S {\displaystyle S} is isomorphic to R / ker φ {\displaystyle R/\ker \varphi }.