Multiplication modules and tensor product

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4 Citations (Scopus)

Abstract

All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) modules to be a faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) module. Necessary and sufficient conditions for the tensor product of pure (resp. invertible, large, small, join principal) submodules of multiplication modules to be a pure (resp. invertible, large, small, join principal) submodule are also considered.

Original languageEnglish
Pages (from-to)305-327
Number of pages23
JournalBeitrage zur Algebra und Geometrie
Volume47
Issue number2
Publication statusPublished - 2006

Keywords

  • Cancellation module
  • Flat module
  • Invertible submodule
  • Join principal submodule
  • Large submodule
  • Multiplication module
  • Projective module
  • Pure submodule
  • Small submodule
  • Tensor product

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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