On Weakly 1-Absorbing Primary Ideals of Commutative Rings

Abstract

Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing primary ideal. A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or c ∈ √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 primary ideals of commutative rings.