Is it true that two polynomial rings are not isomorphic iff the rings are not isomorphic?

Question

Here in the exercice, I have to show that $(Z[t],+, . )$ and $(Q[t],+, .) $ are not isomorphic.

I know the answer! I am simply wondering if it would be true that, showing that $(Z,+, . )$ and $(Q,+, . )$ are not isomorphic is sufficient to say that the polynomial rings are also not isomorphic.

If not, can you find me a counter example?

thank you!