A note on $k$-nil radicals in BCI-algebras
Bull. Korean Math. Soc. 1997 Vol. 34, No. 2, 205-209
Sung Min Hong and Xiaolong Xin
Gyeongsang National University, Northwest University
Abstract : Let $A$ be a subset of a BCI-algebra $X$. We show that the $k$-nil radical of $A$ is the union of branches, and prove that (1) if $A$ is an ideal then the $k$-nil radical $[A;k]$ is a $p$-ideal of $X$; (2) if $A$ is a subalgebra, then the $k$-nil radical $[A;k]$ is a closed $p$-ideal, and hence a strong ideal of$X$.
Keywords : $k$-nil radical, atom, branch, (closed) ideal, $p$-ideal, strong ideal
MSC numbers : 03G25, 06F35, 16N99
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