Talk:Splitting of prime ideals in Galois extensions
|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
Problem with section "Computing the factorization"
There seems to be a contradiction. At the beginning, it is said that "such a \theta is guarantied to exist by the primitive element theorem" (which is true by the Van der Waerden construction, but is irrelevant in my opinion), and near the end of the section, they say that "there is not always such \theta satisfying the above hypotheses". I believe that the hypotheses relative to \theta (that is, "L is generated over K by \theta") should be replaced by O_L = O_K[\theta]. Mike.
Some time back I wrote the section describing the theorem about how to compute the factorisation of an ideal. I'm wondering if anyone knows whether for any given prime ideal P, it is always possible to find an appropriate θ so that the corresponding conductor is prime to P, and therefore it is possible to compute the factorisation of P? Or are there some ideals which can't be tackled by this method? Dmharvey 11:52, 20 April 2006 (UTC)
- Thanks to Ron Evans for supplying an answer to this question. I have incorporated it into the text. Dmharvey 21:35, 11 April 2007 (UTC)