ScholarLens Back to search
2007•Communications in AlgebraRequires access

When Summands of Completely Decomposable Modules Are Completely Decomposable

Pat Goeters

Open publisher page 2 citations

Abstract

We examine when summands of completely decomposable modules over a domain R are again completely decomposable. We show that this is the case if R is an h-local Prüfer domain. If R is 1-dimensional Noetherian, then the problem reduces locally if almost all localizations are integrally closed. If R is 1-dimensional Noetherian and local, then the integral closure of R must have at most two maximal ideals.

About this research paper

What this paper is about

We examine when summands of completely decomposable modules over a domain R are again completely decomposable. We show that this is the case if R is an h-local Prüfer domain. If R is 1-dimensional Noetherian, then the problem reduces locally if almost all localizations are integrally closed. If R is 1-dimensional Noetherian and local, then the integral closure of R must have at most two maximal ideals.

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We examine when summands of completely decomposable modules over a domain R are again completely decomposable. We show that this is the case if R is an h-local Prüfer domain. If R is 1-dimensional Noetherian, then the problem reduces locally if almost all localizations are integrally closed. If R is 1-dimensional Noetherian and local, then the integral closure of R must have at most two maximal ideals.

Key concepts: Noetherian, Integrally closed, Mathematics, Closure (psychology), Local ring, Pure mathematics, Integral domain, Domain (mathematical analysis)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
When Summands of Completely Decomposable Modules Are Completely Decomposable — Research Paper | ScholarLens