I'm almost sure the question has already been asked but i don't know the english terminologies...
I have in my lecture that :
$A$ a ring.
$A$ is a field iff $A[t]$ is principal.
I'm anoyed because I think we can do better. It seems that $ \mathbb R [t] $ is euclidean. So, shoudln't be that theorem stated like that :
$A$ is a field iff $A[t]$ is euclidean.
what do you think ?
I think that in my lectures, we are dealing with rings with a unity, commutative and integral.