Residual submodules of multiplication modules

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11 Citations (Scopus)

Abstract

Let R be a commutative ring with identity and M an R-module. We introduce and give some properties and characterizations of the concepts of Mcancellation, M-weak cancellation, M-meet principal, and M-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule.

Original languageEnglish
Pages (from-to)405-422
Number of pages18
JournalBeitrage zur Algebra und Geometrie
Volume46
Issue number2
Publication statusPublished - 2005

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Keywords

  • Cancellation ideal
  • Meet-principal ideal
  • Multiplication module
  • Residual submodule

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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