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.

13B22, 13H05

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - Sep 21 2018

Keywords

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

ASJC Scopus subject areas

  • General

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