Generalized SIP-modules

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TAŞDEMİR Ö., KARABACAK F.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol.48, no.4, pp.1137-1145, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.15672/hjms.2018.572
  • Journal Name: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1137-1145
  • Keywords: SIP, GSIP, injective module, direct sum, V-ring, INTERSECTION, SUBMODULE, RINGS
  • Anadolu University Affiliated: Yes

Abstract

We say an R-module M has the generalized summand intersection property (briefly GSIP), if the intersection of any two direct summands is isomorphic to a direct summand. This is a generalization of SIP modules. In this note, the characterization of this property over rings and modules is investigated and some useful propositions obtained in SIP modules are generalized to GSIP modules.