On 2-absorbing primary ideals in commutative rings

DOI10.4134/BKMS.2014.51.4.1163zbMATH Open1308.13001arXiv2002.12608OpenAlexW2037365288MaRDI QIDQ2877821

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Publication date: 25 August 2014

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Abstract: Let R be a commutative ring with $1eq0$. 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 $a,b,cinR$ and $0eqabcinI,$ then $abinI$ or $cinsqrtI$. 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.

Full work available at URL: https://arxiv.org/abs/2002.12608

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