Content of a polynomial

Definition
Let $$R$$ be a commutative unital ring and $$f \in R[x]$$ be a polynomial. The content of $$f$$ is defined as the ideal of $$R$$ generated by the coefficients of $$f$$.

In the case where $$R$$ is a gcd domain (for instance, where $$R$$ is a Bezout domain or a unique factorization domain), the content of $$f$$ is defined as the greatest common divisor of all the coefficients of $$f$$. Note that the greatest common divisor is completely determined (upto associates) by the ideal generated by the coefficients: it is the generator of the smallest principal ideal containing that ideal.

In the case that $$R$$ is a Bezout domain, the content of $$f$$ is in fact the generator of the ideal generated by all the coefficients.

Related notions
A primitive polynomial over a ring is a polynomial such that the ideal generated by the coefficients is not contained in any proper principal ideal. Equivalently, the greatest common divisor of the coefficients is $$1$$.