[GAP Forum] Proof of Existence of Unique Monic Polynomial of Minimal Degree

Minh Vaughn matmackaizer at yahoo.ca
Wed Mar 19 04:46:47 GMT 2008

I would be grateful for a proof of the following problem:

Suppose R is a unique factorization domain, and suppose S is an integral domain which is integral over R.  Then for every element s in S there is a UNIQUE monic polynomial P in R[x] of MINIMAL degree, such that P(s) = 0.

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