Lemma 115.5.5. Let $k$ be a field. Let $F, G \in k[X, Y]$ be homogeneous of degrees $d, e$. Assume $F, G$ relatively prime. Then multiplication by $G$ is injective on $S = k[X, Y]/(F)$.
Proof. This is one way to define “relatively prime”. If you have another definition, then you can show it is equivalent to this one. $\square$
Comments (0)