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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 , and are introduced, and the concepts of -support and -support are also introduced. Several related properties are investigated. Characterizations of -subalgebra of type are discussed, and conditions for an -subalgebra of type to be an -subalgebra of type are considered.

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