群环中零因子元素的概率

IF 0.7 Q2 MATHEMATICS

International Journal of Group Theory Pub Date : 2021-10-25 DOI:10.22108/IJGT.2021.126694.1664

M. Salih, M. Haval

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引用次数: 1

摘要

设R是一个具有恒等的非平凡有限交换环，G是一个非平凡群。我们用P(RG)表示有限群环RG中随机选择的两个元素之积为零的概率。我们证明了P(RG) <0.25当且仅当RG不同构于Z2C2, Z3C2, Z2C3。进一步给出了p (RG)的上界和下界。特别地，我们给出了P(RG)的一般公式，其中R是特征P的有限域，|G|≤4。

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On the probability of zero divisor elements in group rings

Let R be a non trivial finite commutative ring with identity and G be a non trivial group. We denote by P(RG) the probability that the product of two randomly chosen elements of a finite group ring RG is zero. We show that P(RG) <0.25 if and only if RG is not isomorphic to Z2C2, Z3C2, Z2C3. Furthermore, we give the upper bound and lower bound for P(RG). In particular, we present the general formula for P(RG), where R is a finite field of characteristic p and |G| ≤ 4.

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来源期刊

International Journal of Group Theory MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

30 weeks

期刊介绍： International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.