# 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.

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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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