Pseudo subalgebras and pseudo filters in pseudo BE-algebras

Sun Shin Ahn, Young Joo Seo, Young Bae Jun

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)4964-4972
Number of pages9
JournalAIMS Mathematics
Volume8
Issue number2
DOIs
StatePublished - 2023

Keywords

  • (atomic) pseudo BE-algebra
  • (atomic) pseudo filter
  • pseudo atom
  • pseudo subalgebra

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