Definition:Primitive Polynomial (Ring Theory)

Definition
Let $\Q \left[{X}\right]$ be the ring of polynomial forms over the field of rational numbers in the indeterminate $X$.

Let $\Z \left[{X}\right]$ be the ring of polynomial forms over the integral domain of integers in the indeterminate $X$.

Let $f \in \Q \left[{X}\right]$ be such that:
 * $(1): \quad f \in \Z \left[{X}\right]$
 * $(2): \quad \operatorname{cont} \left({f}\right) = 1$

where $\operatorname{cont} \left({f}\right)$ is the content of $f$.

That is:
 * $(1): \quad$ All the coefficients of $f$ are integers


 * $(2): \quad$ The greatest common divisor of the coefficients of $f$ is equal to $1$.

Then $f$ is described as primitive.