Pure submodules of multiplication modules

Majid M. Ali*, David J. Smith

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2004


  • 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


Dive into the research topics of 'Pure submodules of multiplication modules'. Together they form a unique fingerprint.

Cite this