Complete Distributivity
Michael R. Darnel · 2021
Recall that a completely distributive lattice is a lattice is which the general distributive law, ⋁ I ⋀ J g ij = ⋀ IJ ⋁ I g i,f ( i ) , holds whenever the indicated joins and meets exist, regardless of the size of the sets I and J. Any totally ordered set is a completely distributive lattice and so there do exist completely distributive ℓ-groups.