Lattices with Unique Complements
نویسنده
چکیده
Introduction. 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 [l](1)) or ortho-complemented (G. Birkhoff [l]) or atomic (G. Birkhoff and M. Ward [l]), then unique complementation implies distributivity and the lattice is a Boolean algebra. In spite of these results, I shall show here that the theorem is not true in general. Indeed, the following counter theorem is proved:
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