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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.

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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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