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.

I'm having some trouble solving this homework problem and understanding what the hint is trying to tell me.

Suppose $K$ is a field extension of $F$ of finite degree. Prove that if $\alpha$ is in $K$, then there is an irreducible polynomial $f(x)$ in $F[x]$ having a as a root. (Hint: If $[K : F]=n$, consider $1,a,a^2,...,a^n$)

share|improve this question

1 Answer 1

Here's a little hint: the family of $1,a,a^2,\dots$ generates a subring of $K$ which is also a $F$-vector space, so subspace of $K$ as $F$-vector space.

From this you could easily conclude using a little of linear algebra.

share|improve this answer

Your Answer

 
discard

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.