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

Asked Jan 24 '18 at 10:43

Active Jan 24 '18 at 10:43

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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!

asked Jan 24 '18 at 10:43

Marine Galantin

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yes ! that is what i searched, i ve also heard about the Zariski problem but I don't understand the solution :/ moreover I don't find many documentation on this topic – Marine Galantin Jan 24 '18 at 10:50
moreover i am asking for the reverse direction – Marine Galantin Jan 24 '18 at 13:24

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

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