Lattices with Unique Complements
R. P. Dilworth · Birkhäuser Boston eBooks · 1990
For several years one of the outstanding problems of lattice theory has been the following: Is every lattice with unique complements a Boolean algebra ? Any number of weak additional restrictions are sufficient for an affirmative answer. For example, if a lattice is modular (G. Bergman [1]( 1 )) or ortho-complemented (G. Birkhoff [1]) or atomic (G. Birkhoff and M. Ward [1]), then unique complementation implies distributivity and the lattice is a Boolean algebra. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.