The Image of an Ideal Under a Surjective Ring Homomorphism is an Ideal
Problem 532
Let $R$ and $S$ be rings. Suppose that $f: R \to S$ is a surjective ring homomorphism.
Prove that every image of an ideal of $R$ under $f$ is an ideal of $S$.
Namely, prove that if $I$ is an ideal of $R$, then $J=f(I)$ is an ideal of $S$.
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