Similarity classes of 3x3 matrices over a local principal ideal ring

TL;DR

This paper classifies similarity classes of 3x3 matrices over local principal ideal rings and provides an explicit generating function for counting these classes over finite quotients.

Contribution

It introduces a detailed analysis of similarity classes over local principal ideal rings and derives an explicit generating function for finite quotients.

Findings

Explicit classification of similarity classes over local principal ideal rings

Derived a generating function for counting classes over finite quotients

Enhanced understanding of matrix similarity in algebraic structures

Abstract

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.