A variation of supplemented modules

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Bilhan G., Güroğlu A. T.

Turkish Journal of Mathematics, vol.37, no.3, pp.418-426, 2013 (SCI-Expanded, Scopus, TRDizin) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.3906/mat-1108-20
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.418-426
  • Keywords: Modules, omega-supplemented, Dedekind domain
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Over a general ring, an R-module is w-supplemented if and only if amply w-supplemented. It is proved that over a local Dedekind domain, all modules are w-supplemented and over a non-local Dedekind domain, an R-module M is w-supplemented if and only if Soc(M) « M or M = S0 ⊕ (⊕iεI K), where S0 is a torsion, semisimple submodule of M and K is the field of quotients of R. © TÜBİTAK.