The Stacks project

Definition 10.28.2. Let $R$ be a ring. Let $\mathcal{F}$ be a set of ideals of $R$. We say $\mathcal{F}$ is an Oka family if $R \in \mathcal{F}$ and whenever $I \subset R$ is an ideal and $(I : a), (I, a) \in \mathcal{F}$ for some $a \in R$, then $I \in \mathcal{F}$.