Definition:Greatest Common Divisor/Polynomial Ring over Field

Definition
Let $F$ be a field.

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

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

This is denoted $\gcd \set {P, Q} = R$.

Also see

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