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Polynomials over the Rational Field: Euclidean Ring: Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.

Modern Algebra
Ring Theory (XXXIII)
Polynomials over the Rational Field
Euclidean Ring
Irreducible Polynomial

Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.

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Solution Summary

It is the explanation of the following problem:

Let D be a Euclidean ring, F its field of quotients. Prove the Gauss lemma for polynomials with coefficients in D factored as product of polynomials with coefficients in F.
The solution is given in detail.

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