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arXiv · 2510.23094

The completeness and congruences of quasi-Boolean algebras

Xiaohao Liu·Heyan Wang·Wenjuan Chen
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Abstract

Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the number of finite quasi-Boolean algebras and characterize the finite irreducible quasi-Boolean algebras. Second, we show the standard completeness of quasi-Boolean algebras. Finally, we prove that the variety of quasi-Boolean algebras satisfies the congruence extension property and provide a complete characterization of how congruences on a Boolean subalgebra can be extended to the whole quasi-Boolean algebra.

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Xiaohao Liu, Heyan Wang, Wenjuan Chen. 2025-10-27. The completeness and congruences of quasi-Boolean algebras. https://arxiv.org/abs/2510.23094

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