Weakly $S$-2-absorbing ideals

Abstract

summary:Let $R$ be a commutative ring with identity. The notion of $S$-$2$-absorbing ideal was introduced by G. Ulucak, Ü. Tekir, S. Koç (2020) as a generalization of $2$-absorbing ideal. We introduce $a$ weaker version of 2-absorbing ideals by defining the concept of weakly-$S$-2-absorbing ideal. Let $S\subseteq R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-2-absorbing ideal of $R$ if whenever $abc\in I$ for $a,b,c\in R$ then there exists $s\in S$ such that $sab\in I$ or $sbc\in I$ or $sac\in I$. We investigate many properties and characterizations of weakly $S$-2-absorbing ideals