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Topic: Two questions on Lattices
Replies: 5   Last Post: Jun 21, 2011 11:54 AM

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Rash

Posts: 2
From: Malaysia
Registered: 6/20/11
Two questions on Lattices
Posted: Jun 20, 2011 4:33 AM
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1. Theorem. Let L be a finite lattice. For all x and y in L, x<=y if and only if J(x) is a subset of J(y)(J(z)={t join-irreducible: t<=z}).
I know that above theorem is correct for finite distributive lattices, but I'm not sure is it correct for any finite lattice?

2. Any subset of finite lattice is a lattice. Is it correct?



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