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 Smarandache weak $BE$-algebras Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 489-496 https://doi.org/10.4134/CKMS.2012.27.3.489Printed September 1, 2012 Arsham Borumand Saeid Shahid Bahonar University of Kerman Abstract : In this paper, we introduce the notions of Smarandache weak $BE$-algebra, $Q$-Smarandache filters and $Q$-Smarandache ideals. We show that a nonempty subset $F$ of a $BE$-algebra $X$ is a $Q$-Smarandache filter if and only if $A(x,y)\subseteq F$, which $A(x,y)$ is a $Q$-Smarandache upper set. The relationship between these notions are stated and proved. Keywords : $CI$-algebras, $BE$-algebra, Smarandache weak $BE$-algebra, ($Q$-Smarandache) filter, ($Q$-Smarandache) ideal MSC numbers : Primary 06F35, 03G25 Downloads: Full-text PDF

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