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Commutative Rings in Which Every Ideal Is S-2-Absorbing
Rendiconti Del Circolo Matematico Di PalermoIn the present paper, the authors introduce and study the class of \(S\)-2-absorbing rings, which generalize the notion of 2-absorbing rings with respect to a multiplicative subset \(S\) of a commutative ring \(R\) with identity. An ideal \(I\) of \(R\) disjoint from \(S\) is called \textit{\(S\)-2-absorbing} if there exists an element \(s \in S\) such
Hwankoo Kim
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On 2-absorbing ideals of commutative semirings
Journal of Algebra and Its Applications, 2021Let S be a commutative semiring with unity different than zero. In this paper, we study the concept of 2-absorbing ideals of S which can be considered as a generalization of prime ideals. Among others, it is shown that the radical of a 2-absorbing ideal is also a 2-absorbing ideal and there are at most 2 prime k-ideals of S that are minimal over a 2 ...
Leena Sawalmeh, Mohammed Saleh
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On 2-Absorbing Ideals in Commutative Rings with Unity
Lobachevskii Journal of Mathematics, 2018Let \(R\) 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 \(ac\in I\).
Dubey, M. K., Aggarwal, P.
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On completely 2-absorbing ideals of N-groups
Journal of Discrete Mathematical Sciences and Cryptography, 2021We introduce the notion of completely 2-absorbing (denoted by, c-2-absorbing) ideal of an N-group G, as a generalization of completely prime ideal of module over a right near-ring N. We obtain that, for an ideal I of a monogenic N-group G, if (I: G) is a c-2-absorbing ideal of N, then I is a c-2- absorbing ideal of G.
Taptee Sahoo +4 more
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JP Journal of Algebra, Number Theory and Applications, 2017
Summary: The origin of the present study is the paper [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)], where the author studied the concept of 2-absorbing ideals in commutative rings. Many classical theorems on ideals have been used to arrive at the results.
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Summary: The origin of the present study is the paper [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)], where the author studied the concept of 2-absorbing ideals in commutative rings. Many classical theorems on ideals have been used to arrive at the results.
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ON 2-ABSORBING IDEALS OF NONCOMMUTATIVE RINGS
JP Journal of Algebra, Number Theory and Applications, 2018Summary: Let \(R\) be a noncommutative ring with identity. We define the notion of a 2-absorbing ideal and show that if the ring is commutative, then the notion is the same as the original definition that of \textit{A. Badawi} [Bull. Aust. Math. Soc. 75, No. 3, 417--429 (2007; Zbl 1120.13004)].
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On 2-absorbing and weakly 2-absorbing principally right primary ideals
2021Summary: Let \(R\) be a noncommutative ring. The purpose of this note is to investigate the concept of 2-absorbing (resp., weakly 2-absorbing) p right primary ideals generalizing 2-absorbing (resp., weakly 2-absorbing) ideals of noncommutative rings. From [\textit{G. Birkenmeier} et al., Monatsh. Math. 117, No.
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On 2-Absorbing Quasi-Primary Ideals in Commutative Rings
Communications in Mathematics and Statistics, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tekir, Unsal +3 more
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