Content formula - Knowlpedia

Content formula: Let $R$ be a UFD and let $f,g\in R[x]$ . Choose elements $c(f),c(g),c(fg)$ generating the coefficient ideals (the content ideals). Then

c(fg)\sim c(f)c(g),

i.e., the chosen generator of the content ideal of $fg$ is associate to the product of the chosen generators for $f$ and $g$ . In particular, the product of primitive polynomials is primitive.

Remarks

Here content is computed in the polynomial ring over a UFD. The formula implies that the product of two primitive polynomials is primitive and is a standard ingredient in Gauss's content lemma.