Fuzzy Quotient Structures of\\ $BCK$-algebras Induced by Fuzzy $BCK$-filters

Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 27-36 Printed March 1, 2006

Young Bae Jun Gyeongsang National University

Abstract : In this paper, we establish a generalization of fundamental homomorphism theorem in $BCK$-algebras by using fuzzy $BCK$-filters. We prove that if $\mu$ (resp. $\nu$) is a fuzzy $BCK$-filter of a bounded $BCK$-algebra $X$ (resp. $Y$), then ${{X\times Y}\over {\mu \times \nu}}\cong {X/{\mu}}\times {Y/{\nu}}$; and if $\mu$ is a fuzzy $BCK$-filter and $F$ is a $BCK$-filter in a bounded $BCK$-algebra $X$ such that $F/{\mu}$ is a $BCK$-filter of $X/{\mu}$, then ${{X/{\mu}}\over {F/{\mu}}}\cong {X/F}.$