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 ${{X/{\mu}}\over {F/{\mu}}}\cong {X/F}.$
Keywords : (fuzzy) $BCK$-filter, fuzzy quotient $BCK$-algebra
MSC numbers : 06F35, 03G25, 03B52
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