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Research Article | Open Access

Structure of a chain ring as a ring of matrices over a Galois ring

Yousef Alkhamees( ), Badr Alhajouj
Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia
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Abstract

The structure of a finite chain ring has already been described by Wirt in 1972 and others later. The purpose of this article is to describe another structure of a finite chain ring as a ring of square matrices over Galois ring using the companion matrix of a certain Eisenstein polynomial over Galois ring. Such a companion matrix generates the unique maximal ideal of the corresponding matrix chain ring.

Keywords

local ringchain ringGalois ringcompanion matrix
CLC number: 16L30, 16P20, 16P30

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AIMS Mathematics
Volume 7 Issue 9,
September 2022
Pages 15824-15833
DOI: 10.3934/math.2022866

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Cite this article:
Alkhamees Y, Alhajouj B. Structure of a chain ring as a ring of matrices over a Galois ring. AIMS Mathematics, 2022, 7(9): 15824-15833. https://doi.org/10.3934/math.2022866

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Received: 16 February 2022
Revised: 24 May 2022
Accepted: 12 June 2022
Published: 15 September 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)