**GCD Over A Ring and Over Its Field of Fractions**

In this section, we consider polynomials over a unique factorization domain *R*, typically the ring of the integers, and over its field of fractions *F*, typically the field of the rational numbers, and we denote *R* and *F* the rings of polynomials in a set of variables over these rings.

Read more about this topic: Greatest Common Divisor Of Two Polynomials

### Other articles related to "gcd over a ring and over its field of fractions, gcd":

**GCD Over A Ring and Over Its Field of Fractions**- Proof That GCD Exist For Multivariate Polynomials

... In the previous section we have seen that the

**GCD**of polynomials in R may be deduced from

**GCD**'s in R and in F ... proof shows that this allows to prove the existence of

**GCD**'s in R, if they exist in R and in F ... In particular, if

**GCD**'s exist in R, and if X is reduced to one variable, this proves that

**GCD**'s exist in R (Euclid's algorithm proves the existence of

**GCD**'s in F) ...

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