Let $R$ be the ring of all continuous real valued functions on a completely regular space $X $, that is $R:=C (X)$, and let $0\not=I $ be an ideal of $ R $ and $\{ I_i \}_{ i\in A } $ be a family of ideals of $ R $. I am looking for a condition (preferably an equivalent )on $I $ such that if $I\subseteq \sum_{ i\in A } I_i $ then we can deduced that there exists $j\in A $ such that $I\subseteq I_j $?
For example minimal ideals have this property.