Generalizations of 𝒩 -Subalgebras in BCK/BCI-Algebras Based on Point 𝒩 -Structures

Abstract

The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of $𝒩$-subalgebras of types $(\in ,q_k),(\in ,\in \vee q_k)$, and $(q,\in \vee q_k)$ are introduced, and the concepts of $q_k$-support and $\in \vee q_k$-support are also introduced. Several related properties are investigated. Characterizations of $𝒩$-subalgebra of type $(\in ,\in \vee q_k)$ are discussed, and conditions for an $𝒩$-subalgebra of type $(\in ,\in \vee q_k)$ to be an $𝒩$-subalgebra of type $(\in ,\in )$ are considered.