Let $R$ and $S$ be rings of characteristic $0$.
If $R$ and $S$ are isomorphic as a ring, then, why $R/7R$ is isomorphic to $S/7S$ as a ring ?
My try :
Let $φ:R→S$ be an isom and $π: S→S/7S$ be natural projection.
If we could prove $ker(π・φ)＝7S$・・・①, it's done. But I'm having trouble proving ① formally. Another approach is also appreciated.