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On the generalization of pseudo p-closure in pseudo BCI-algebras | ||
| Journal of Hyperstructures | ||
| دوره 14، شماره 1، 2025، صفحه 25-35 اصل مقاله (1.62 M) | ||
| نوع مقاله: Review paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.16086.1058 | ||
| نویسندگان | ||
| Padena Pirzadeh Ahvazi1؛ Habib Harizavi* 1؛ Tayebeh Koochakpoor2 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran Unevesity of Ahvaz | ||
| 2Department of Mathematics, Faculty of Sciences, Payame noor University, Tehran, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| BCI-algebra؛ pseudo BCI-algebra؛ minimal elements؛ nilpotent elements؛ closure operation | ||
| مراجع | ||
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[1] L. C. Ciungu Pseudo BCI-algebras With Derivations, Department of Mathematics, University of Iowa, USA. 14 (2019), 5-17. [2] G. Dymek, On pseudo BCI-algebras, Annales Universalistic Mariae Curie-Sklodowska Lublin Poloia., 1 (2015), 59-71. [3] G. Dymek, On two classes of pseudo BCI-algebras, Discussions Math, General Algebra and Application, 31 (2011), 217-229. [4] G. Dymek, p-semisimple pseudo BCI-algebras, J. Mult-Valued Logic Soft Comput., 19 (2012), 461-474. [5] W. A. Dudek, Y. B. Jun, Pseudo BCI-algebras, East Asian Math. J., 24 (2008), 187-190. [6] H. Hrizavi, P-closure in pseudo BCI-algebras, Journal of Algebraic Systems, 7 (2) (2020), 155-165. [7] Y. Imai and K. Iseki, On axiom system of propositional calculi, Proc. Japan. Acad., 42 (1966), 19-22. [8] K. Iseki, An algebra related with a propositional calculus, Japan. Acad., 42 (1966), 26-29. [9] Y. B. Jun, H. S. Kim and J. Neggers, On pseudo-ideals of pseudo BCI-algebras, Matemat. Bech., 58 (2006), 39-46. [10] Y. H. Kim and K. S. So, On Minimality in pseudo BCI-algebras, Commun. Korean. Math. Soc., 1 (2012), No. 1, 7-13. [11] J. Meng and Y. B. Jun, BCK-Algebras, Kyung Moon Sa Co., Seoul, 1994. [12] H. Moussei, H. Harizavi and R. A. Borzooei, p-closure ideals in BCI-algebras, Soft Computing, 22, (2018), 7901-7908. [13] H. Yisheng, BCI-Algebra, Published by Science Press, 2006. | ||
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