Some remarks on multiplication and projective modules

Majid M. Ali, David J. Smith

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The associated ideal θ(M) and the trace ideal T(M) of a module M play analogous but distinct roles in the study of multiplication and projective modules respectively. We further investigate both and show in particular that faithful multiplication and projective modules have common properties. We use a method based on Anderson's characterizations of multiplication modules which enables new proofs of theorems on multiplication modules of El Bast, Low, Smith and Smith, and then, also enables similar results for projective modules.

Original languageEnglish
Pages (from-to)3897-3909
Number of pages13
JournalCommunications in Algebra
Volume32
Issue number10
DOIs
Publication statusPublished - 2004

Fingerprint

Multiplication Module
Projective Module
M-ideal
Faithful
Trace
Distinct
Module
Theorem

Keywords

  • Multiplication module
  • Projective module
  • Pure ideal
  • Trace of a module

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Some remarks on multiplication and projective modules. / Ali, Majid M.; Smith, David J.

In: Communications in Algebra, Vol. 32, No. 10, 2004, p. 3897-3909.

Research output: Contribution to journalArticle

Ali, Majid M. ; Smith, David J. / Some remarks on multiplication and projective modules. In: Communications in Algebra. 2004 ; Vol. 32, No. 10. pp. 3897-3909.
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