Let $m_i $, $i \in I,$ be an infinite family of maximal ideas in a commutative ring with identity(It is not Noetherian in general). When dose there exist $j \in I$ such that $\cap_{i\not= j} m_i\subseteq m_j$. Or is any equivalent condition for this?

Let $m_i $, $i \in I,$ be an infinite family of maximal ideals in a commutative ring with identity  (it is not supposed to be Noetherian). When does there exist $j \in I$ such that $\cap_{i\not= j} m_i\subseteq m_j$? Or is there any equivalent condition for this?