Bulletin of the
Korean Mathematical Society BKMS

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