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

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 ring
• chain ring
• galois ring
• companion matrix