# 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.

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com December 15, 2022, 5:59 pm ad1c9bdddfhttps://brainmass.com/math/ring-theory/118216

#### 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.

$2.49