Prove or disprove: The image of a ring homomorphism $\phi:R\to S$ is an ideal in $S$.
I only see examples where they use the image of an ideal, but I don't think this is the case for my question.
At first I tried using the ideal test, and I had a feeling that it wasn't working out the way it should, so now I am trying to find a counterexample. Any ideas for a simple counterexample?