Talk:Distributivity (order theory)

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I've copied much of the "Distributivity laws for complete lattices" section into an new article completely distributive completely distributive lattice and marked it as a stub. Perhaps it would be better to call the new article complete distributivity or completely distributive lattice, but I used the link used in this article as a starting point. Please help make that article better and, in particular, add citations. --Malcohol 08:59, 17 October 2006 (UTC)
 * In the light of this, I'm planning on removing much of the more specific content on complete distributivity from this article. Are their any objections to this?--Malcohol 09:28, 17 October 2006 (UTC)
 * Done--Malcohol 14:35, 23 October 2006 (UTC)

The definition of distributive semilattice is always satisfied in any lattice. Just take a'=x and b'=x. —Preceding unsigned comment added by 24.130.241.83 (talk) 01:30, 9 December 2008 (UTC)
 * No, it might be the case that $$a$$ and $$b$$ are incomparable to $$x$$ but nonetheless $$a \wedge b \leq x$$. A specific counterexample can be found by considering the lattice $$M_3$$.82.19.52.143 (talk) 21:45, 18 May 2011 (UTC)