Talk:Distributivity (order theory)

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)