12 Cancellation modules and homogeneous idealization

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Abstract

All rings are commutative with identity and all modules are unital. In this article, we characterize cancellation modules and use this characterization to give necessary and sufficient conditions for the sum and intersection of cancellation modules to be cancellation. We introduce and give some properties of the concept of [image omitted] join principal submodules. We show that via the method of idealization most questions concerning [image omitted] (weak) cancellation and [image omitted] join principal modules can be reduced to the ideal case.

Original languageEnglish
Pages (from-to)3524-3543
Number of pages20
JournalCommunications in Algebra
Volume35
Issue number11
DOIs
Publication statusPublished - Nov 2007

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Keywords

  • (Weak) Cancellation module
  • 1 Join principal submodule
  • 1(Weak) Cancellation module
  • Idealization
  • Multiplication module
  • Projective module

ASJC Scopus subject areas

  • Algebra and Number Theory

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