On Weakly 1-absorbing Primary Ideals of Commutative Rings

Abstract

Let R be a commutative ring with $1\ne 0$. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal. A proper ideal $I$ of $R$ is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c\in R$ and $0\ne abc\in I,$ then $ab\in I$ or $c\in \sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. Furthermore, we give the correct version of a result on 1-absorbing ideals of commutative rings.

It is submitted on September,2019