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 am stuck by a problem in Jacobson I for a long time. It seems not too difficult. Hope anyone can help me out. It is on page 300.

Let $E$ be a cyclic extension of dimension $n$ over $F$ and $\eta$ be a generator of $\text{Gal }E/F$. Let $r|n$, $n=rm$ and suppose $c$ is a non-zero element of $F$ such that $c^r=N_{E/F}(u)$ for some $u\in E$. Show that there exists a $v$ in the unique subfield $K$ of $\text{Gal }E/F$ of dimensionality $m$ such that $c=N_{K/F}(v)$.

This is a theorem due to Albert. I also checked his book: Structure of Algebra. But I really can not understand what he was saying. Can we solve this problem just by Galois theory? Thank you very much.

share|improve this question
1  
I finally know how to solve this problem. See my page sunlimingbit.wordpress.com/2012/04/11/… –  Slm2004 Apr 11 '12 at 15:06

Your Answer

 
discard

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

Browse other questions tagged or ask your own question.