modular law

Let ${}_{R}M$ be a left $R$-module with submodules $A,B,C$, and suppose$C\subseteq B$. Then

$$C+(B\cap A)=B\cap (C+A)$$

This result shows that the submodules of ${}_{R}M$, partially ordered by inclusion, form a modular lattice with $\cap$ as the meet and $+$ as the join (http://planetmath.org/Join).