Prime ideal splitting in field extension and its normal closure

Asked May 17 '11 at 16:30

Active Jan 12 '13 at 06:02

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The question is:

Let L / K be a finite (not necessarily Galois) extension of algebraic number fields and N / K the normal closure of L / K. Show that a prime ideal p of K is totally split in L if and only if it is totally split in N. Hint: Use the double coset decomposition H\G/GP, where G = G(N/K), H = G(N/L) and GP , is the decomposition group of a prime ideal P over p.

My question is how to use this hint to solve this problem; please give me some advice.

edited Jan 12 '13 at 06:02

Joseph Quinsey

asked May 17 '11 at 16:30

dust

7

This is dealt with in my answer here. Voting to close. – Arturo Magidin May 17 '11 at 16:32
3

And in my answer here: http://math.stackexchange.com/questions/33573/ramification-in-a-tower-of-extensions/33579#33579 – Alex B. May 17 '11 at 16:36
@Alex:Thanks but I can not see your answer there...it seems that there is something wrong with the internet... – dust May 17 '11 at 17:25
I can; the link works perfectly fine. Maybe something wrong on your end. – Arturo Magidin May 17 '11 at 18:39

Prime ideal splitting in field extension and its normal closure

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