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 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 ideals of commutative rings.
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