Hi,(adsbygoogle = window.adsbygoogle || []).push({});

how can I show that afield extensionisnormal?

Here is a concrete example:

[tex]L|K [/tex] is normal, whereas [tex]L=\mathbb F_{p^2}(X,Y) [/tex] and [tex] K= \mathbb F_p(X^p,Y^p) [/tex].

[tex] p [/tex] is a prime number of course.

I have to show that every irreducible polynomial in [tex]K[X,Y][/tex] that has a root in [tex]L[/tex] completely factors into linear factors over [tex]L[/tex].

But this is not simply in my case, because elements in [tex]K[X,Y]=\mathbb F_p(X^p,Y^p)[X,Y] [/tex] has the form:

[tex] \frac{g(x,y)}{h(x,y)}, \quad h(x,y)\neq 0, \quad g,h \in K[X,Y] [/tex]

Bye,

Brian

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Normal field extension

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**