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).

Title modular law ModularLaw 2013-03-22 12:50:42 2013-03-22 12:50:42 yark (2760) yark (2760) 7 yark (2760) Theorem msc 16D10 ModularLattice