On weakly S-2-absorbing filters of lattices

Abstract

Let $\pounds$ be a bounded distributive lattice and $S$ a join closed subset of $\pounds$. Following the concept of weakly $S$-$2$-absorbing submodules, we define weakly $S$-$2$-absorbing filters of $\pounds$. Let $P$ be a filter of $\pounds$ disjoint with $S$. We say that $P$ is a weakly $S$-$2$-absorbing filter of $\pounds$ if there is a fixed $s \in S$ such that for all $x, y, z \in \pounds$ if $1 \neq x \vee y \vee z \in P$, then $s \vee x \vee y \in P$ or $s \vee y \vee z \in P$ or $s \vee x \vee z \in P$. We will make an intensive investigate the basic properties and possible structures of these filters.