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Rash
Posts:
2
From:
Malaysia
Registered:
6/20/11


Two questions on Lattices
Posted:
Jun 20, 2011 4:33 AM


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 joinirreducible: 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?



