On the generalization of pseudo p-closure in pseudo BCI-algebras - Padena Pirzadeh Ahvazi; Habib Harizavi; Tayebeh Koochakpoor (Journal of Hyperstructures, 2025)
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.