Pairs of Modules over a Principal Ideal Domain

TL;DR

This paper investigates pairs of finitely generated modules over a principal ideal domain, focusing on their matrix representations, equivalence relations, invariants, and canonical forms to classify such module pairs.

Contribution

It introduces new equivalence relations and canonical forms for pairs of modules over a principal ideal domain, advancing classification methods.

Findings

Established invariants for module pairs

Defined canonical forms for module pairs

Provided classification criteria for module pairs

Abstract

We study pairs of finitely generated modules over a principal ideal domain and their corresponding matrix representations. We introduce equivalence relations for such pairs and determine invariants and canonical forms.