𝒩-Structures Applied to Commutative Ideals of BCI-Algebras

Abstract

The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object’s symmetries. In order to provide a mathematical tool for dealing with negative information, a negative-valued function came into existence along with N-structures. In the present analysis, the notion of N-structures is applied to the ideals, especially the commutative ideals of BCI-algebras. Firstly, several properties of N-subalgebras and N-ideals in BCI-algebras are investigated. Furthermore, the notion of a commutative N-ideal is defined, and related properties are investigated. In addition, useful characterizations of commutative N-ideals are established. A condition for a closed N-ideal to be a commutative N-ideal is provided. Finally, it is proved that in a commutative BCI-algebra, every closed N-ideal is a commutative N-ideal.