\begin{definition}[Definition:Greatest Common Divisor/Polynomial Ring over Field]
Let $F$ be a field.
Let $P, Q, R \in F \left[{X}\right]$ be polynomials.
Then $R$ is '''the greatest common divisor''' of $P$ and $Q$ {{iff}} it is a monic greatest common divisor.
This is denoted $\gcd \left({P, Q}\right) = R$.
\end{definition}