Pseudo subalgebras and pseudo filters in pseudo BE-algebras

Sun Shin Ahn; Young Joo Seo; Young Bae Jun; Sun Shin Ahn; Young Joo Seo; Young Bae Jun

doi:10.3934/math.2023248

AIMS Mathematics

2023, Volume 8, Issue 2: 4964-4972. doi: 10.3934/math.2023248

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Research article

Pseudo subalgebras and pseudo filters in pseudo BE-algebras

1.
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea
2.
Research Institute for Natural Sciences, Department of Mathematics, Hanyang University, Seoul 04763, Korea
3.
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Received: 10 September 2022 Revised: 13 November 2022 Accepted: 20 November 2022 Published: 12 December 2022
MSC : 03G25, 06F35

As a generalization of BE-algebras, the pseudo BE-algebra was introduced by Borzooei et al., and the notions of pseudo subalgebras and pseudo filters in pseudo BE-algebras were defined, and some related properties were investigated. In order to further study pseudo subalgebras and pseudo filters in pseudo BE-algebras, concepts of pseudo atom, atomic pseudo BE-algebra, and atomic pseudo filter are introduced and related studies are conducted. The conditions under which pseudo-filters can be created using a nonempty set, and the conditions under which non-unit elements can be pseudo-atoms are explored. Characterization of atomic pseudo BE-algebra is discussed, and conditions are provided under which pseudo subalgebra can be pseudo filters. The relationship between a set of pseudo atoms and a pseudo subalgebra is considered, and the conditions under which a pseudo filter can be atomic are found.
- (atomic) pseudo BE-algebra,
- pseudo subalgebra,
- (atomic) pseudo filter,
- pseudo atom
Citation: Sun Shin Ahn, Young Joo Seo, Young Bae Jun. Pseudo subalgebras and pseudo filters in pseudo BE-algebras[J]. AIMS Mathematics, 2023, 8(2): 4964-4972. doi: 10.3934/math.2023248

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Abstract

As a generalization of BE-algebras, the pseudo BE-algebra was introduced by Borzooei et al., and the notions of pseudo subalgebras and pseudo filters in pseudo BE-algebras were defined, and some related properties were investigated. In order to further study pseudo subalgebras and pseudo filters in pseudo BE-algebras, concepts of pseudo atom, atomic pseudo BE-algebra, and atomic pseudo filter are introduced and related studies are conducted. The conditions under which pseudo-filters can be created using a nonempty set, and the conditions under which non-unit elements can be pseudo-atoms are explored. Characterization of atomic pseudo BE-algebra is discussed, and conditions are provided under which pseudo subalgebra can be pseudo filters. The relationship between a set of pseudo atoms and a pseudo subalgebra is considered, and the conditions under which a pseudo filter can be atomic are found.

References

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