有限交换环上的广义概率

IF 0.5 Q3 MATHEMATICS

International Electronic Journal of Algebra Pub Date : 2022-08-05 DOI:10.24330/ieja.1156662

S. Rehman, Muhammad Naveed Shaheryar

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引用次数: 0

摘要

设$R$是一个有单位的有限交换环，且$x\在R$中。我们研究了R$的两个随机选择的元素(有替换)的乘积等于x$的概率。我们用$Prob_x (R)$表示这个概率。我们确定了这个概率的一些界，并在此基础上得到了有限交换环的一些表征。此外，我们确定了当$R=\mathbb{Z}_m\乘以\mathbb{Z}_n$时$Prob_x (R)$的显式计算公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Generalized Probability in Finite Commutative Rings

Let $R$ be a finite commutative ring with unity and $x\in R$. We study the probability that the product of two randomly chosen elements (with replacement) of $R$ equals $x$. We denote this probability by $Prob_x (R)$. We determine some bounds for this probability and also obtain some characterizations of finite commutative rings based on this probability. Moreover, we determine the explicit computing formulas for $Prob_x (R)$ when $R=\mathbb{Z}_m\times \mathbb{Z}_n$.

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来源期刊

International Electronic Journal of Algebra MATHEMATICS-

CiteScore

0.90

自引率

16.70%

发文量

审稿时长

36 weeks

期刊介绍： The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.