Idealization and theorems of D. D. Anderson

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7 Citations (Scopus)

Abstract

All rings are commutative with identity and all modules are unital. Anderson proved that a submodule N of an R-module M is multiplication (resp. join principal) if and only if 0(+)N is a multiplication (resp. join principal) ideal or R(M). The idealization of M. In this article we develop more fully the tool of idealization of a module, particularly in the context of multiplication modules, generalizing Anderson's theorems and discussing the behavior under idealization of some ideals and some submodules associated with a module.

Original languageEnglish
Pages (from-to)4479-4501
Number of pages23
JournalCommunications in Algebra
Volume34
Issue number12
DOIs
Publication statusPublished - Dec 1 2006

Keywords

  • Flat module
  • Idealization
  • Join principal submodule
  • Multiplication module
  • Projective module
  • Pure submodule

ASJC Scopus subject areas

  • Algebra and Number Theory

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