Definition:Greatest Common Divisor/Polynomial Ring over Field

Definition
Let $F$ be a field.

Let $P,Q,R\in F[X]$ be polynomials.

Then $R$ is the greatest common divisor of $P$ and $Q$ if it is a monic greatest common divisor.

Also see

 * Polynomials over Field have Unique Monic GCD
 * Polynomial Forms over Field is Euclidean Domain