D-extending modules

DURĞUN Y.

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, cilt.49, sa.3, ss.914-920, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.15672/hujms.460241
  • Dergi Adı: HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.914-920
  • Anahtar Kelimeler: D-extending modules, d-closed submodules, semiartinian modules, CLOSED SUBMODULE
  • Çukurova Üniversitesi Adresli: Evet

Özet

A submodule N of a module M is called d-closed if M/N has a zero socle. D-closed submodules are similar concept to s-closed submodules, which are defined through non-singular modules by Goodearl. In this article we deal with modules with the property that all d-closed submodules are direct summands (respectively, closed, pure). The structure of a ring over which d-closed submodules of every module are direct summand (respectively, closed, pure) is studied.