On the generalization of pseudo p-closure in pseudo BCI-algebras

Articles in Press

Document Type : Review paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran Unevesity of Ahvaz

2 Department of Mathematics, Faculty of Sciences, Payame noor University, Tehran, Iran

Abstract

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.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 26 January 2025

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