Additional information concerning the content of the product of polynomials

A. I. Uzkov

Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 395-398.

Résumé

Let $\operatorname{Cont}_Af$ denote the content of the polynomial $f$ in several unknowns with coefficients from the extension $R$ of the ring $A$. We prove that for arbitrary polynomials $f$ and $g$ the relation $$ \operatorname{Cont}\nolimits_Afg\cdot(\operatorname{Cont}g)^m=\operatorname{Cont}f\cdot(\operatorname{Cont}g)^{m+1}, $$ holds, where $m+1$ is the number of the nonzero terms of the polynomial $f$.