Well-covered unitary Cayley graphs of matrix rings over finite fields and applications

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-04-09 DOI:10.1016/j.ffa.2024.102428

Shahin Rahimi, Ashkan Nikseresht

引用次数: 0

Abstract

Suppose that F is a finite field and $R = M_{n} (F)$ is the ring of n-square matrices over F. Here we characterize when the Cayley graph of the additive group of R with respect to the set of invertible elements of R, called the unitary Cayley graph of R, is well-covered. Then we apply this to characterize all finite rings with identity whose unitary Cayley graph is well-covered or Cohen-Macaulay.

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有限域上矩阵环的井盖单元 Cayley 图及其应用

假设 F 是有限域，R=Mn(F) 是 F 上的 n 方矩阵环。在此，我们将描述 R 的加法群关于 R 的可逆元素集的 Cayley 图（称为 R 的单元 Cayley 图）何时被很好地覆盖。然后，我们将其应用于表征所有具有同一性的有限环，这些有限环的单元 Cayley 图都是井盖图或 Cohen-Macaulay 图。

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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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.