COFINITELY GENERALIZED WEAK SUPPLEMENTED MODULES

Eryılmaz F., Eren Ş.

JOURNAL OF SCIENCE AND ARTS, no.4, pp.673-684, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Publication Date: 2017
  • Journal Name: JOURNAL OF SCIENCE AND ARTS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.673-684
  • Keywords: Cofinite Submodule, Cofinitely Generalized Weak Supplemented Module, Generalized Cover, Semilocal Ring, RINGS, SEMIPERFECT, EXTENSIONS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.