# Separability of finitely generated projectives over commutative ring

A class $\mathcal{C}$ of $R$-modules is called

-separative if $A \oplus A \simeq A \oplus B \simeq B \oplus B$ implies $A \simeq B$ for each $A,B \in \mathcal{C}$

-cancelative if $A \oplus C \simeq B \oplus C$ implies $A \simeq B$ for all $A,B,C \in \mathcal{C}$.

According to literature, if $R$ is commutative then the class of finitely generated projectives over $R$ is separative iff it is cancelative. Even though I keep finding it as 'easy to see' in literature I seem unable to prove separative => cancelative. I would be grateful for any hint.

-