Title

Direct-Sum Behavior Of Modules Over One-Dimensional Rings

Abstract

Let R be a reduced, one-dimensional Noetherian local ring whose integral closure is finitely generated over R. Since is a direct product of finitely many principal ideal domains (one for each minimal prime ideal of R), the indecomposable finitely generated-modules are easily described, and every finitely generated-module is uniquely a direct sum of indecomposable modules. In this article we will see how little of this good behavior trickles down to R. Indeed, there are relatively few situations where one can describe all of the indecomposable R-modules, or even the torsion-free ones. Moreover, a given finitely generated module can have many different representations as a direct sum of indecomposable modules. © 2011 Springer Science+Business Media, LLC.

Publication Date

12-1-2011

Publication Title

Commutative Algebra: Noetherian and Non-Noetherian Perspectives

Number of Pages

251-275

Document Type

Article; Book Chapter

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-1-4419-6990-3_10

Socpus ID

84879669072 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84879669072

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