Constructing indecomposable integrally closed modules over a two-dimensional regular local ring

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Abstract

In this article, we construct integrally closed modules of rank two over a two-dimensional regular local ring. The modules are explicitly constructed from a given complete monomial ideal with respect to a regular system of parameters. Then we investigate their indecomposability. As a consequence, we have a large class of indecomposable integrally closed modules whose Fitting ideal is not simple. This gives an answer to Kodiyalam's question.

Original languageEnglish
Pages (from-to)879-907
Number of pages29
JournalJournal of Algebra
Volume556
DOIs
Publication statusPublished - Aug 15 2020

Keywords

  • Indecomposable module
  • Integral closure
  • Monomial ideal
  • Regular local ring

ASJC Scopus subject areas

  • Algebra and Number Theory

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