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The Prime Congruences on Quasi-Boolean Algebras.

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Title: The Prime Congruences on Quasi-Boolean Algebras.
Authors: Liu, Xiaohao1 liuxiaohao@mail.ujn.edu.cn, Lv, Yajie1 jasslyj@mail.ujn.edu.cn, Chen, Wenjuan2 wjchenmath@gmail.com
Source: IAENG International Journal of Applied Mathematics. Jun2026, Vol. 56 Issue 6, p2168-2173. 6p.
Subjects: Congruence lattices, Boolean algebra, Homomorphisms
Abstract: As a generalization of Boolean algebras, quasi-Boolean algebras have been introduced. This paper is devoted to the investigation of prime congruences defined on quasi-Boolean algebras. First, we discuss the relationship between congruences and weak filters of quasi-Boolean algebras. Second, we establish the connection between strong proper prime congruences and strong proper weak prime weak filters of quasi-Boolean algebras. Finally, we discuss the properties of prime congruences on quasi-Boolean algebras under homomorphisms. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: The Prime Congruences on Quasi-Boolean Algebras.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Xiaohao%22">Liu, Xiaohao</searchLink><relatesTo>1</relatesTo><i> liuxiaohao@mail.ujn.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lv%2C+Yajie%22">Lv, Yajie</searchLink><relatesTo>1</relatesTo><i> jasslyj@mail.ujn.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Chen%2C+Wenjuan%22">Chen, Wenjuan</searchLink><relatesTo>2</relatesTo><i> wjchenmath@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jun2026, Vol. 56 Issue 6, p2168-2173. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Congruence+lattices%22">Congruence lattices</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+algebra%22">Boolean algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Homomorphisms%22">Homomorphisms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: As a generalization of Boolean algebras, quasi-Boolean algebras have been introduced. This paper is devoted to the investigation of prime congruences defined on quasi-Boolean algebras. First, we discuss the relationship between congruences and weak filters of quasi-Boolean algebras. Second, we establish the connection between strong proper prime congruences and strong proper weak prime weak filters of quasi-Boolean algebras. Finally, we discuss the properties of prime congruences on quasi-Boolean algebras under homomorphisms. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        StartPage: 2168
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        Type: general
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      – SubjectFull: Homomorphisms
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      – TitleFull: The Prime Congruences on Quasi-Boolean Algebras.
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            NameFull: Liu, Xiaohao
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              M: 06
              Text: Jun2026
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              Y: 2026
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