On 2-absorbing ideals in commutative rings with unity
type: Item
instance of: scholarly article
title: On 2-absorbing ideals in commutative rings with unity
zbMATH Open document ID: 1390.13006
DOI: 10.1134/S1995080218020087
author: Y. Aharonov
published in: Lobachevskii Journal of Mathematics
publication date: 2018-06-25T00:00:00Z
review text: Let \(R\) be a commutative ring with non-zero identity. In the paper under review, the authors introduce the concept of \(n\)-weakly prime ideal which is a generalization of prime ideals. A proper ideal \(I\) of \(R\) is an \(n\)-weakly prime if for \(a, b, c \in R\), \(abc \in I\) implies that \(ab\in I\) or \(bc\in I\) or \(ac\in I\). The authors prove number of results concerning to \(n\)-weakly prime ideals.
reviewed by: Siamak Yassemi
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 16Y60
zbMATH DE Number: 6893810
zbMATH Keywords: commutative ring
zbMATH Keywords: 2-absorbing ideal
zbMATH Keywords: irreducible ideal
zbMATH Keywords: regular ring
MaRDI profile type: Publication
cites work: Q4679047
cites work: UNIQUE FACTORIZATION AND BIRTH OF ALMOST PRIMES
cites work: On 2-absorbing ideals of commutative rings
cites work: On weakly 2-absorbing ideals of commutative rings
cites work: Onn-Absorbing Ideals of Commutative Rings
cites work: On 2-absorbing submodules over commutative rings
cites work: On 2-absorbing primary submodules of modules over commutative ring with unity
cites work: On \(n\)-absorbing submodules of modules over commutative rings
cites work: 2-absorbing and \(n\)-weakly prime submodules
cites work: Generalizations of Prime Ideals
cites work: On the 2-absorbing ideals
full work available at URL: s1995080218020087
OpenAlex ID: W2800195508
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description: scientific article; zbMATH DE number 6893810