# Math Help - Field Theory - General Qiestion

1. ## Field Theory - General Qiestion

I am studying field theory.

A general question I have is the following:

Let $E \supseteq F$ be fields and let $u \in E$.

Now, if I determine an irreducible polynomial in F[x] such that f(u) = 0 in E, can I conclude that I have found the minimal polynomial of u over F.

Peter

2. ## Re: Field Theory - General Qiestion

No because the minimal polynomial is monic. You may have a constant multiple of the minimal polynomial. If you have an irreducible monic polynomial in F[x] such that f(u) = 0 in E, then you can conclude you have found the minimal polynomial of u over F.

3. ## Re: Field Theory - General Qiestion

Yes, you are right of course ... Thanks!!!

Peter