# Infinite modular lattices [closed]

A finite lattice $$L$$ is called modular if and only if its elements satisfy the following modular identity: For all $$x,y,z\in L$$ such that $$x\leq z$$, we have $$x\vee(y\wedge z)=(x\vee y)\wedge z$$.

How can we define an infinite modular lattice? Does the criterion remain the same in the infinite case as well?

## closed as off-topic by user21820, Adrian Keister, The Count, postmortes, GNUSupporter 8964民主女神 地下教會Jun 25 at 22:28

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Of course, it's a condition that has to be checked for all triples $$x,y,z$$ with $$x \le z$$, but it's a simple "algebraic" condition between a few elements. No distinction is needed (or made) for the case where $$L$$ itself is infinite or not.