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March 9th, 2014, 04:25 AM  #1 
Newbie Joined: Mar 2014 Posts: 4 Thanks: 0  conjugates of a polynomial
Hi, 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 https://upload.wikimedia.org/wikiped...polynomial.pdf , pp. 56 (thm. 3.1). Thx. N.B. There was an error in the link in my previous post. I would be grateful it be deleted. 

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