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Foulis-Holland theorem for implicative-orthomodular lattices

2024/03/25 by Ciungu, Lavinia Corina
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2403.16762

Abstract

We introduce the notion of distributivity for implicative-orthomodular lattices, proving an analogue result of the Foulis-Holland theorem. Based on this result, we characterize the distributive implicative-orthomodular lattices. Moreover, we define the center of an implicative-orthomodular lattice as the set of all elements that commute with all other elements, and we prove that the center is an implicative-Boolean algebra. Additionally, we give new characterizations of implicative-orthomodular lattices.

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