Let $K$ be a field. Let $L/K$ and $E/L$ be finite extensions. Let $α$ be an element of E. Let $N_{E/K}(α)$ be the norm of $α$, i.e. the determinant of the regular representaion matrix of $α$. It is well known that $N_{E/K}(α)$ $=$ $N_{L/K}(N_{E/L}(α))$ if $E/K$ is separable. I tried to find a proof of this formula in inseparable extensions, but failed. Where can I find it? It'd be also nice if someone provides a sketch of the proof, here.


The proof can be found here.

  • $\begingroup$ Thanks. That's a nice proof. $\endgroup$ – Makoto Kato May 8 '12 at 2:06
  • $\begingroup$ By the way, I think the proof of Lemma 1.1 in the above link is incorrect. $\endgroup$ – Makoto Kato May 8 '12 at 2:38
  • $\begingroup$ I found another proof. See my comments here(math.stackexchange.com/questions/50737/… ). $\endgroup$ – Makoto Kato May 14 '12 at 0:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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