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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 -subalgebras of types (∈,qk),(∈,∈∨qk), and (q,∈∨qk) are introduced, and the concepts of qk-support and ∈∨qk-support are also introduced. Several related properties are investigated. Characterizations of -subalgebra of type (∈,∈∨qk) are discussed, and conditions for an -subalgebra of type (∈,∈∨qk) to be an -subalgebra of type (∈,∈) are considered.

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