$k$-nil radical in BCI-algebras II
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 499-505
Y. B. Jun, S. M. Hong, E. H. Roh
Gyeongsang National University, Gyeongsang National University, Gyeongsang National University
Abstract : This paper is a continuation of [3]. We prove that if $A$ is a quasi-associative (resp. an implicative) ideal of a BCI-algebra $X$ then the $k$-nil radical of $A$ is a quasi-associative (resp. an implicative) ideal of $X$. We also construct the quotient algebra $X/[A;k]$ of a BCI-algebra $X$ by the $k$-nil radical $[A;k]$, and show that if $A$ and $B$ are closed ideals of BCI-algebras $X$ and $Y$ respectively, then $$X/[A;k]\times Y/[B;k]\cong X\times Y/[A\times B;k].$$
Keywords : $k$-nil radical, (closed) ideal, quasi-associative ideal, implicative ideal, quotient algebra
MSC numbers : 03G25, 06F35
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