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A note on symmetric differences of orthomodular lattices

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Abstract

There exist two distinct symmetric differences in a non Boolean orthomodular lattice. Let $L$ be an orthomodular lattice. Then $L$ is a Boolean algebra if and only if one symmetric difference is equal to the other. An orthomodular lattice $L$ is Boolean if and only if one of two symmetric differences of $L$ is associative.

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