# On commuting probability of finite rings

@article{Dutta2015OnCP,
title={On commuting probability of finite rings},
author={Jutirekha Dutta and Dhiren Basnet and Rajat Kanti Nath},
journal={arXiv: Rings and Algebras},
year={2015}
}
• Published 28 October 2015
• Mathematics, Computer Science
• arXiv: Rings and Algebras
15 Citations
• Mathematics
• 2018
Let $R$ be a finite ring. The commuting probability of $R$, denoted by $\Pr(R)$, is the probability that any two randomly chosen elements of $R$ commute. $R$ is called an $n$-centralizer ring if it
• Mathematics
• 2017
The non-commuting graph $\Gamma_R$ of a finite ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R \setminus Z(R)$ and two distinct vertices $a$ and $b$ are adjacent if
• Walaa Nabil Taha FasfousReza Sharafdini
• Mathematics
• 2020
The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$ .
• Mathematics
• 2016
Let $S, K$ be two subrings of a finite ring $R$. Then the generalized non-commuting graph of subrings $S, K$ of $R$, denoted by $\Gamma_{S, K}$, is a simple graph whose vertex set is $(S \cup K) • Mathematics • 2017 Let$S$be a subring of a finite ring$R$and$C_R(S) = \{r \in R : rs = sr \;\forall\; s \in S\}$. The relative non-commuting graph of the subring$S$in$R$, denoted by$\Gamma_{S, R}$, is a simple • Mathematics • 2020 The study on probability theory in finite rings has been an interest of various researchers. One of the probabilities that has caught their attention is the probability that two elements of a ring • Mathematics • 2016 The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different subrings of a finite non-commutative ring equals a given • R. K. Nath • Mathematics Boletim da Sociedade Paranaense de Matemática • 2019 Let$R$be a nite non-commutative ring with center$Z(R)$. The commuting graph of$R$, denoted by$\Gamma_R$, is a simple undirected graph whose vertex set is$R\setminus Z(R)$and two distinct • David Dolzan • Mathematics Bulletin of the Australian Mathematical Society • 2022 Abstract Let R be a finite ring and let${\mathrm {zp}}(R)\$ denote the nullity degree of R, that is, the probability that the multiplication of two randomly chosen elements of R is zero. We
• Mathematics
• 2017
The aim of this paper is to study the probability that the commutator of an arbitrarily chosen pair of elements, each from two different additive subgroups of a finite non-commutative ring equals a