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}
}
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15 Citations
Background Citations
7

15 Citations

Commuting probabilities of $n$-centralizer finite rings

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…

On non-commuting graph of a finite ring

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…

Various spectra and energies of commuting graphs of finite rings

  • Walaa Nabil Taha FasfousR. K. NathReza 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 $xy = yx$ .…

On generalized non-commuting graph of a finite ring

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)…

Relative non-commuting graph of a finite ring

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…

On the probability and graph of some finite rings of matrices

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…

On commuting probability of finite rings II

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…

A note on super integral rings

  • 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…

THE PROBABILITY OF ZERO MULTIPLICATION IN FINITE RINGS

  • 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…

A generalization of commuting probability of finite rings

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…

References

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The relative commutativity degree of a subgroup $$H$$H of a finite group $$G$$G, denoted by $$\Pr (H, G)$$Pr(H,G), is the probability that an element of $$G$$G commutes with an element of $$H$$H. In…

Finite rings with many commuting pairs of elements

We investigate the set of values attained by Pr(R), the probability that a random pair of elements in a nite ring R commute. A key tool is a new notion of isoclinism for rings, and an associated…

ON COMMUTATIVITY OF FINITE RINGS

Properties of external direct product of two rings are based on properties of component rings. These results are used to construct special types of rings. Any ring which is a cyclic additive group is…

On the Relative Commutativity Degree of a Subgroup of a Finite Group

The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of relative commutativity degree of a subgroup H of a…

On a lower bound of commutativity degree

The commutativity degree of a finite group G, denoted by Pr(G), is the probability that a randomly chosen pair of elements of G commute. The object of this paper is to derive a lower bound for Pr(G)…

ON GENERALIZED RELATIVE COMMUTATIVITY DEGREE OF A FINITE GROUP

Given any two subgroups H and K of a finite group G, and an element g ∈ G, the aim of this article is to study the probability that the commutator of an arbitrarily chosen pair of elements (one from…

ON THE COMMUTING PROBABILITY IN FINITE GROUPS

A CHARACTERISATION OF CERTAIN FINITE GROUPS OF ODD ORDER

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The commutativity degree of a finite group is the probability that two randomly chosen group elements commute. The main object of this paper is to obtain a characterization for all finite groups of…

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On some problems of a statistical group-theory. IV