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modular lattice

Defines: 
modular
Synonym: 
Dedekind lattice
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

06C05 no label found

Comments

Maybe the article should mention that in order to show that a lattice is modular it is really only necessary to show that x<=z implies x∨(y∧z)>=(x∨y)∧z since x<=z implies x∨(y∧z)<=(x∨y)∧z for any lattice.

If you would like the entry to be changed, please post a correction (preferably without strange characters).

Feel free to add "modular inequality" to the encyclopedia, with "modular lattice" as the parent. Also, prove this inequality in your entry, if possible.

should "modular inequality" not be attached to "lattice", since it applies to any lattice and not just modular lattices?

It is true that modular inequality applies to any lattice. But so do other lattice inequalities, like the distributive inequalities, which are covered under a separate entry whose parent is "distributive lattice".

I would recommend either putting it in a separate entry (with modular lattice as a parent), or file a correction to the "modular lattice" entry so it is mentioned under there.

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