Meaning of a symbol regarding field.

Question

I was going through a problem in Dummit and Foote's Abstract Algebra. That problem involves two subfields $K$ and $E$, and $K=Q(a^{1/n})$. In that problem they have a hint that $N_{K/E}(a^{1/n})\in E$. I have never seen the last symbol $N_{K/E}(a^{1/n})$. It will be really great if someone can tell me what this symbol means.

Answer 1

On pages 581 - 582, it is defined in Exercise 17:

Let $K/F$ be any finite extension and let $\alpha\in K$. Let $L$ be a Galois extension of $F$ containing $K$ and let $H \leq \text{Gal}(L/F)$ be the subgroup corresponding to $K$. Define the norm of $\alpha$ from $K$ to $F$ to be $$ N_{K/F}(\alpha) = \prod_{\sigma}\sigma(\alpha), $$ where the product is taken over all the embeddings of $K$ into an algebraic closure of $F$.