A note on k-nil radicals in BCI-algebras

Hong et al. [2] and Jun et al. [4] introduced the notion of k-nil radical in a BCI-algebra, and investigated its some properties. In this paper, we discuss the further properties on the k-nil radical. Let A be a subset of a BCI-algebra X. We show that the k-nil radical of A is the union of branches. We prove that if A is an ideal then the k-nil radical [A;k] is a p-ideal of X, and that if A is a subalgebra, then the k-nil radical [A;k] is a closed p-ideal, and hence a strong ideal of X.

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