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March 9th, 2014, 04:22 AM   #1
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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. 5-6 (thm. 3.1).

Thx.
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March 9th, 2014, 04:41 AM   #2
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Re: conjugates of a polynomial

There is a mistake in the link in this post. Please, see the most recent post with the same subject. (hope this post will be deleted).
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March 11th, 2014, 04:00 AM   #3
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Re: conjugates of a polynomial

In fact, the correct link has moved to
https://upload.wikimedia.org/wikipedia/ ... -07-12.pdf (pp. 5-6).
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