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Pseudo subalgebras and pseudo filters in pseudo BE-algebras

Authors :
Sun Shin Ahn
Young Joo Seo
Young Bae Jun
Source :
AIMS Mathematics. 8:4964-4972
Publication Year :
2023
Publisher :
American Institute of Mathematical Sciences (AIMS), 2023.

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.

Subjects

Subjects :
General Mathematics

Details

ISSN :
24736988
Volume :
8
Database :
OpenAIRE
Journal :
AIMS Mathematics
Accession number :
edsair.doi...........f4810d4fb51c28788f0a4d559967037e