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March 9th, 2014, 04:25 AM   #1
Joined: Mar 2014

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conjugates of a polynomial

I think I have proved the following theorem, but I'm not sure. I would greatly appreciate some comments, and also a reliable source about this theorem or something close to it (I imagine that something like this has already been proved).
"Let f be an irreducible polynomial over a field K, and assume that g divides f in some extension of K. Let M be the splitting field of f over K, and L be the field generated by the coefficients of g over K (so K<L<M). Then the product of the elements of the set of the distinct conjugates of g, where belong to Gal(M/K), is equal to , with and ."
My supposed proof can be found in , pp. 5-6 (thm. 3.1).


N.B. There was an error in the link in my previous post. I would be grateful it be deleted.
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conjugates, polynomial

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