I think I have proved the following theorem:(adsbygoogle = window.adsbygoogle || []).push({});

"If R is an integral domain, x is integral of degree n over R, and K is the fraction field of R, then the intersection of R[x] with K is included in 1/n R[X] (the set of elements r/n where r belongs to R). Furthermore, if R is Dedekind, then this intersection is R."

My simple proof can be found here:

https://upload.wikimedia.org/wikipedia/commons/d/de/Bensimhoun-1.lemma_in_Galois_Theory-2.RxInterQuotR-3.conjugates_of_polynomial.pdf [Broken] (pp. 3--5).

My question is: Where can I found reliable references to this theorem, or at least reliable references to another theorem implying it ?

Thx.

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# About integral extensions

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