Pure submodules of multiplication modules

Majid M. Ali, David J. Smith

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are considered. We also give two descriptions for the trace of a pure submodule of a multiplication module.

Original languageEnglish
Pages (from-to)61-74
Number of pages14
JournalBeitrage zur Algebra und Geometrie
Volume45
Issue number1
Publication statusPublished - 2004

Fingerprint

Multiplication Module
Idempotent
Annihilator
Multiplication
Trace
If and only if

Keywords

  • Flat module
  • Idempotent submodule
  • Multiplication module
  • Projective module
  • Pure submodule
  • Radical of a module
  • Trace of a module

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Pure submodules of multiplication modules. / Ali, Majid M.; Smith, David J.

In: Beitrage zur Algebra und Geometrie, Vol. 45, No. 1, 2004, p. 61-74.

Research output: Contribution to journalArticle

Ali, Majid M. ; Smith, David J. / Pure submodules of multiplication modules. In: Beitrage zur Algebra und Geometrie. 2004 ; Vol. 45, No. 1. pp. 61-74.
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