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
Canonical name	ModularLaw
Date of creation	2013-03-22 12:50:42
Last modified on	2013-03-22 12:50:42
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	7
Author	yark (2760)
Entry type	Theorem
Classification	msc 16D10
Related topic	ModularLattice