Can ring homomorphisms be characterized as ring maps such that preimage of any ideal is an ideal? – math.stackexchange.com

It's a well know fact that preimage of ideals by ring homomorphism are also ideals. Is the reciprocal true? I.e., let $f:R\to S$ be a map between the rings $R$ and $S$ s.t. $f^{-1}(I)\vartriangleleft ...

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