Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring

TL;DR

This paper constructs explicit examples of indecomposable integrally closed modules of any rank over a two-dimensional regular local ring, expanding the understanding of their structure and existence.

Contribution

It provides a new explicit construction method for indecomposable integrally closed modules of arbitrary rank, extending previous results and strengthening the theoretical framework.

Findings

Constructed explicit indecomposable modules from complete monomial ideals

Established structural and numerical properties of these modules

Proved the existence of large classes of such modules with non-simple ideals

Abstract

In this paper, we construct indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring. The modules are quite explicitly constructed from a given complete monomial ideal. We also give structural and numerical results on integrally closed modules. These are used in the proof of indecomposability of the modules. As a consequence, we have a large class of indecomposable integrally closed modules of arbitrary rank whose ideal is not necessarily simple. This extends the original result on the existence of indecomposable integrally closed modules and strengthens the non-triviality of the theory developed by Kodiyalam.