The completeness and congruences of quasi-Boolean algebras
Logic
2025-10-28 v1
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.
Keywords
Cite
@article{arxiv.2510.23094,
title = {The completeness and congruences of quasi-Boolean algebras},
author = {Xiaohao Liu and Heyan Wang and Wenjuan Chen},
journal= {arXiv preprint arXiv:2510.23094},
year = {2025}
}