Communications of the
Korean Mathematical Society CKMS

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