Results 211 to 220 of about 15,241 (255)

Invariance theorems for a class of systems of random nonlinear equations over an arbitrary finite ring with left unity

Cybernetics and Systems Analysis, 2008
A class of homogenous systems of random nonlinear equations over an arbitrary finite ring with left unity is considered. The author analyzes the invariance boundaries for limit factorial moments of nonzero solutions, the limit distribution of the number of nonzero solutions, and the geometrical structure of the set of nonzero solutions of the system as
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Solving the problem of invariance of probabilistic characteristics for a priori solvable systems of random nonlinear equations over a finite commutative ring with unity

Cybernetics and Systems Analysis, 2010
A class of a priori solvable systems of random non-linear equations over a finite commutative ring with unity is considered. The questions of the bounds of the invariance domains for the limit factorial moments and, accordingly, the limit distribution of the number of solutions that are different from a fixed solution to a given system and also the ...
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Some Commutativity Conditions for Rings with Unity

Results in Mathematics, 1991
Let \(R\) be a ring with 1. The following conditions are equivalent: 0) \(R\) is commutative. 1) There exists a non-negative integer \(m\) such that, given \(x,y\in R\), \(\{1-h(x^ m y)\}[x,x^ m y-f(yx^ m)]\cdot\{1- g(x^ my)\}=0\) for some \(f(X)\in X^ 2\mathbb{Z}[X]\) and \(g(X),h(X)\in XZ[X]\).
Komatsu, Hiroaki, Tominaga, Hisao
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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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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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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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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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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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Universal adjacency spectrum of the looped zero divisor graph for a finite commutative ring with unity

Asian-European Journal of Mathematics, 2022
For a finite undirected looped graph [Formula: see text], the universal adjacency matrix [Formula: see text] is a linear combination of the adjacency matrix [Formula: see text], the degree matrix [Formula: see text], the identity matrix [Formula: see text] and the all-ones matrix [Formula: see text], that is [Formula: see text], where [Formula: see ...
Bajaj, Saraswati, Panigrahi, Pratima
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