A variation of supplemented modules

BİLHAN G., Guroglu A. T.

TURKISH JOURNAL OF MATHEMATICS, cilt.37, sa.3, ss.418-426, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.3906/mat-1108-20
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.418-426
  • Anahtar Kelimeler: Modules, omega-supplemented, Dedekind domain
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

Over a general ring, an R-module is omega-supplemented if and only if amply omega-supplemented. It is proved that over a local Dedekind domain, all modules are omega-supplemented and over a non-local Dedekind domain, an R-module M is omega-supplemented if and only if Soc(M) << M or M = S-0 circle plus (circle plus(i is an element of I) K), where S-0 is a torsion, semisimple submodule of M and K is the field of quotients of R.