The completeness and congruences of quasi-Boolean algebras

2025/10/27 by Liu, Xiaohao, Wang, Heyan, Chen, Wenjuan
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2510.23094

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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