On the generalization of pseudo p-closure in pseudo BCI-algebras
In this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed. Also, a necessary and sufficient condition for an element to be minimal; and for pseudo BCI-algebra to be...
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| Format: | Article |
| Language: | English |
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University of Mohaghegh Ardabili
2025-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_3661_b7963bcccaa61a7169cd521f008b9b0c.pdf |
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| author | Padena Pirzadeh Ahvazi Habib Harizavi Tayebeh Koochakpoor |
| author_facet | Padena Pirzadeh Ahvazi Habib Harizavi Tayebeh Koochakpoor |
| author_sort | Padena Pirzadeh Ahvazi |
| collection | DOAJ |
| description | In this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed. Also, a necessary and sufficient condition for an element to be minimal; and for pseudo BCI-algebra to be nilpotent are given. It is proved that the set of all nilpotent elements of a pseudo BCI-algebra A, denoted by NA, is the least closed pseudo-ideal with the property gcl(NA)=NA. Finally, it is shown that the mentioned notion, as a function, defines a closure operation on pseudo-ideals. |
| format | Article |
| id | doaj-art-aa8b36817cc4476aa997e8f839d64fd9 |
| institution | Kabale University |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-aa8b36817cc4476aa997e8f839d64fd92025-08-20T03:28:54ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662025-06-01141253510.22098/jhs.2024.16086.10583661On the generalization of pseudo p-closure in pseudo BCI-algebrasPadena Pirzadeh Ahvazi0Habib Harizavi1Tayebeh Koochakpoor2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran Unevesity of AhvazDepartment of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran Unevesity of AhvazDepartment of Mathematics, Faculty of Sciences, Payame noor University, Tehran, IranIn this paper, the notion of generalization of pseudo p-closure, denoted by gcl, is introduced and its related properties are investigated. The gcl of subalgebras and pseudo-ideals is discussed. Also, a necessary and sufficient condition for an element to be minimal; and for pseudo BCI-algebra to be nilpotent are given. It is proved that the set of all nilpotent elements of a pseudo BCI-algebra A, denoted by NA, is the least closed pseudo-ideal with the property gcl(NA)=NA. Finally, it is shown that the mentioned notion, as a function, defines a closure operation on pseudo-ideals.https://jhs.uma.ac.ir/article_3661_b7963bcccaa61a7169cd521f008b9b0c.pdfbci-algebrapseudo bci-algebraminimal elementsnilpotent elementsclosure operation |
| spellingShingle | Padena Pirzadeh Ahvazi Habib Harizavi Tayebeh Koochakpoor On the generalization of pseudo p-closure in pseudo BCI-algebras Journal of Hyperstructures bci-algebra pseudo bci-algebra minimal elements nilpotent elements closure operation |
| title | On the generalization of pseudo p-closure in pseudo BCI-algebras |
| title_full | On the generalization of pseudo p-closure in pseudo BCI-algebras |
| title_fullStr | On the generalization of pseudo p-closure in pseudo BCI-algebras |
| title_full_unstemmed | On the generalization of pseudo p-closure in pseudo BCI-algebras |
| title_short | On the generalization of pseudo p-closure in pseudo BCI-algebras |
| title_sort | on the generalization of pseudo p closure in pseudo bci algebras |
| topic | bci-algebra pseudo bci-algebra minimal elements nilpotent elements closure operation |
| url | https://jhs.uma.ac.ir/article_3661_b7963bcccaa61a7169cd521f008b9b0c.pdf |
| work_keys_str_mv | AT padenapirzadehahvazi onthegeneralizationofpseudopclosureinpseudobcialgebras AT habibharizavi onthegeneralizationofpseudopclosureinpseudobcialgebras AT tayebehkoochakpoor onthegeneralizationofpseudopclosureinpseudobcialgebras |