We do not impose homomorphism must map 1 to 1. The two rings are commutative, unital rings. How to show that the preimage of a prime ideal must not be the whole ring/domain? or show a counter example.
Everything single proof I saw impose $f(1)=1$ for ring homomorphisms but I'm yet to see a counter example where both rings are unital, commutative.
Any help appreciated!