Abstract
It is known that in a lattice with unique complements, the modularity, atomicity, de Morgan, and other conditions imply that the lattice is distributive. It is proved that a compactly generated lattice with unique complements is also Boolean.
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 617–620, November, 1972.
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Salii, V.N. A compactly generated lattice with unique complements is distributive. Mathematical Notes of the Academy of Sciences of the USSR 12, 806–807 (1972). https://doi.org/10.1007/BF01099070
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DOI: https://doi.org/10.1007/BF01099070