Idempotent and nilpotent submodules of multiplication modules

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

All rings are commutative with identity, and all modules are unital. The purpose of this article is to investigate multiplication von Neumann regular modules. For this reason we introduce the concept of nilpotent submodules generalizing nilpotent ideals and then prove that a faithful multiplication module is von Neumann regular if and only if it has no nonzero nilpotent elements and its Krull dimension is zero. We also give a new characterization for the radical of a submodule of a multiplication module and show in particular that the radical of any submodule of a Noetherian multiplication module is a finite intersection of prime submodules.

Original languageEnglish
Pages (from-to)4620-4642
Number of pages23
JournalCommunications in Algebra
Volume36
Issue number12
DOIs
Publication statusPublished - Dec 2008

Fingerprint

Multiplication Module
Idempotent
Prime Submodule
Nilpotent Element
Module
Krull Dimension
Noetherian
Faithful
Unital
Multiplication
Intersection
If and only if
Ring
Zero

Keywords

  • Idempotent submodule
  • Multiplication module
  • Nilpotent submodule
  • Pure submodule
  • Von Neumann regular module

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Idempotent and nilpotent submodules of multiplication modules. / Ali, Majid M.

In: Communications in Algebra, Vol. 36, No. 12, 12.2008, p. 4620-4642.

Research output: Contribution to journalArticle

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