Greatest Common Divisor of Two Polynomials - GCD Over A Ring and Over Its Field of Fractions

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.

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

Greatest Common Divisor Of Two Polynomials - 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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