Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

1) I know K/F is normal if K is a splitting field of some S subset F.

2) K/F is a separable extension if every element of K is separable.

...but am having problems coming up with an extension that can be neither (not 1 and not 2)

share|improve this question
add comment

1 Answer

How about $L=F_5(\root{15}\of t)$ over $K=F_5(t)$? There's an intermediate field $E=F_5(\root5\of t)$ which is inseperable over $K$, and $L$ is not normal over $E$.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.