On D-closed submodules

DURĞUN Y., ÖZDEMİR S.

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, cilt.130, sa.1, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 130 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1007/s12044-019-0537-1
  • Dergi Adı: PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, MathSciNet, zbMATH
  • Anahtar Kelimeler: Closed submodule, flat module, Dickson torsion theory, semiartinian module, proper class, MODULES
  • Çukurova Üniversitesi Adresli: Evet

Özet

A submodule N of a module M is called D-closed if the socle of M/ N is zero. D-closed submodules are similar to S-closed submodules (a generalization of closed submodules) defined through nonsingular modules. First, we describe the smallest proper class (due to Buchsbaum) containing the class of short exact sequences determined byD-closed submodules in terms of that submodule, and showthat it coincides with other classes of modules under certain conditions. Second, we study coprojective modules of this class, called edc-flat modules. We give some equivalent conditions for injective modules to be edc-flat for special rings, and for edc-flat modules to be projective (flat) for any ring.