Foulis-Holland theorem for implicative-orthomodular lattices
Logic
2024-03-26 v1
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.
Keywords
Cite
@article{arxiv.2403.16762,
title = {Foulis-Holland theorem for implicative-orthomodular lattices},
author = {Lavinia Corina Ciungu},
journal= {arXiv preprint arXiv:2403.16762},
year = {2024}
}