Results 221 to 230 of about 15,584 (255)

w_2-ELEMENTS IN A COMMUTATIVE RING WITH UNITY

JP Journal of Algebra, Number Theory and Applications, 2017
Summary: In this paper, we introduce and study \(w_2\)-elements in a commutative ring \(R\) with unity. An element \(0\neq x\in R\) is said to be a \(w_2\)-element of \(R\) if whenever \(xd=x\) for \(1\neq d\in R\), then there exists \(0\neq z\in R\) such that \(zd=zx\).
Kang, Shin Min, Khalid, Waseem, Nazeer, Waqas, Tariq, Tayyab   +3 more
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On 2-Absorbing Ideals in Commutative Rings with Unity

Lobachevskii Journal of Mathematics, 2018
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 \(ac\in I\).
Dubey, M. K., Aggarwal, P.
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Commutative Rings with Unity

1993
The main objects of study in this book are polynomials. Only the most elementary mathematical skills are required to manipulate polynomials. However, in order to develop the theory of Grobner bases it is necessary to work within the larger framework of abstract algebra. The concept of abstract algebra arises from the observation that certain operations
Thomas Becker, Volker Weispfenning
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Application of Commutative Rings with Unity for Construction of Symmetric Encryption System

Cybernetics and Systems Analysis, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weakly local commutativity for rings with unity

Quaestiones Mathematicae, 2019
A ring R is called a left weakly local commutative ring (WLC, for short) if for any a ∈ N (R) and b ∈ R, (ab)2 = ba2b, which is a proper generalization of CN rings.
Bakri Gadelseed, Junchao Wei, Hua Yao
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Spectrally arbitrary patterns over rings with unity

Linear Algebra and its Applications, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Glassett, Jillian L., McDonald, Judith J.   +1 more
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The Ring of Gyges: Overridingness and The Unity of Reason

Social Philosophy and Policy, 1997
Does morality override self-interest? Or does self-interest override morality? These questions become important in situations where there is conflict between the overall verdicts of morality and self-interest, situations where morality on balance requires an action that is contrary to our self-interest, or where considerations of self-interest on ...
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Pure ideals in commutative reduced Gelfand rings with unity

Archiv der Mathematik, 1989
In this paper, pure ideals in the class of all commutative reduced Gelfand rings with unity are classified. Then as an application, we prove that any pure ideal in the ring C(X) of all continuous real valued functions over a completely regular Hausdorff space has the form \(\cap_{x\in K}0_ x \), where K is a closed subset of the Stone- Čech ...
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The algebra of a commutative semigroup over a commutative ring with unity

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1985
SynopsisA new description is provided for the nil radical of the algebra RS of a commutative semigroup S over a commutative ring R with a 1. It is shown that the Jacobson radical of RS is nil if the Jacobson radical of R is nil and that the converse holds in the case where S is periodic.
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Group Homomorphism Generated Near-Rings and Rings: A Unity Not Fixing Each Element of the Group

Communications in Algebra, 2003
Abstract Let (G, +) be a group, not necessarily abelian, and let K be a nontrivial subgroup of G. Let ℋ =  ℋ(G, K) be the additive group generated by Hom (G, K). Then (ℋ(G, K), +, ○) is a d.g. near-ring. If K ≠ G, then ℋ(G, K) cannot contain the unity element of ℰ(G), the near-ring generated by End G.
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