On weakly 2-absorbing ideals of commutative rings (Q2839879)

The aim of this paper is to introduce and study the concept of a \textit{weakly 2-absorbing ideal} of a commutative unital ring \(R\): a proper ideal \(I\) of \(R\) is said to be \textit{weakly 2-absorbing} if whenever \(a,b,c\in R\) and \(0\neq abc\in I\), then either \(ab\in I\) or \(ac \in I\) or \(bc\in I\). In case the condition \(0\neq abc\) is removed, one obtains the concept of a \textit{2-absorbing ideal,} introduced by the first author of this paper in [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)].