Actually Crawley and Dilworth define locally distributive only for strongly atomic lattices. We generalize this definition to an arbitrary complete lattice L in the obvious way: if u is in L let ua be the join of the covers of u; if there are none ua = u. L is locally distributive if ua/u is distributive for each u in L.
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Ralph Freese
Wed May 1 14:43:43 HST 1996