Ring epimorphism $f:R\rightarrow S$, $R$ has finitely many maximal ideals, then $f(J(R))=J(S)$.
Posted by kpax, at math.stackexchange.com,
Suppose $R$ and $S$ are commutative rings with unit, and $f:R\rightarrow S$ is an epimorphism. Prove that: $$f(J(R))\subseteq Jā¦