Abstract
In this short paper we shall prove that every bounded lattice L with the conditions: (c1) 1′ = 0 and (EL): (a · b′)′ = b + a′ · b′ for all a, b ∈ L is a Boolean algebra. This is a more general result than that of Renedo et al. (Proceedings NAFIPS’04, 2004), in which it is proved that every orthocomplemented lattice with (EL) is a Boolean algebra.
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References
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Kondo, M., Dudek, W.A. On bounded lattices satisfying Elkan’s law. Soft Comput 12, 1035–1037 (2008). https://doi.org/10.1007/s00500-007-0270-z
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DOI: https://doi.org/10.1007/s00500-007-0270-z