Let $R$ be a ring and let $I,J,K$ be its ideals. Let $I=(0:J)=\{r\in R \mid rJ = 0 \}$. Then $I$ is called the annihilator of $J$.
Now let $I=(K:J)=\{r\in R \mid rJ \subseteq K \}$. Is there a name for $I$ in this case with respect to $J$? ($I$ is ... of $J$?)