Lattice laws forcing distributivity under unique complementation.
Ranganathan Padmanabhan, WILLIAM S. MCCUNE, Robert Veroff · 2007
Abstract. We give several new lattice identities valid in nonmodular lattices such that a uniquely complemented lattice satisfying any of these identities is necessarily Boolean. Since some of these identities are consequences of modu-larity as well, these results generalize the classical result of Birkhoff and von Neumann that every uniquely complemented modular lattice is Boolean. In particular, every uniquely complemented lattice in M ∨ V(N5), the least non-modular variety, is Boolean. 1.