COFINITELY GENERALIZED WEAK SUPPLEMENTED MODULES

Eryılmaz F., Eren Ş.

JOURNAL OF SCIENCE AND ARTS, sa.4, ss.673-684, 2017 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2017
  • Dergi Adı: JOURNAL OF SCIENCE AND ARTS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.673-684
  • Anahtar Kelimeler: Cofinite Submodule, Cofinitely Generalized Weak Supplemented Module, Generalized Cover, Semilocal Ring, RINGS, SEMIPERFECT, EXTENSIONS
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

Let R be a ring and M be a left R-module. M is called cofinitely generalized weak supplemented (or briefly CGWS-module) if every cofinite submodule of M has a generalized weak supplement in M. In this paper, we give various properties of that kind of modules. It is shown that (1) A module M is CGWS-module if and only if every maximal submodule has a generalized weak supplement in M. (2) The class of cofinitely generalized weak supplemented modules are closed under taking homomorphic images, arbitrary sums, generalized covers and short exact sequences. (3) A ring R is semilocal if and only if every left R-module is a CGWS-module. (4) A commutative domain R is h-semilocal if and only if every torsion R module is cofinitely generalized weak supplemented.