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.
Original language | English |
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Pages (from-to) | 4964-4972 |
Number of pages | 9 |
Journal | AIMS Mathematics |
Volume | 8 |
Issue number | 2 |
DOIs | |
State | Published - 2023 |
Keywords
- (atomic) pseudo BE-algebra
- (atomic) pseudo filter
- pseudo atom
- pseudo subalgebra