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

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 (is an element of,qk), (is an element of,is an element of Vqk), and (q,is an element of Vqk) are introduced, and the concepts of qk-support and is an element of Vqk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type (is an element of, is an element of Vqk) are discussed, and conditions for an N-subalgebra of type (is an element of, is an element of Vqk) to be an N-subalgebra of type (is an element of, is an element of) are considered.