Generalized f-semiperfect Modules

Turkmen B. N., Pancar A.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, vol.4, no.1, pp.85-92, 2013 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 1
  • Publication Date: 2013
  • Journal Name: COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.85-92
  • Keywords: Generalized projective cover, Generalized semiperfect module, Generalized f-semiperfect module
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper we introduce generalized f-semiperfect modules as a generalization of the generalized semiperfect modules. We give various properties of the generalized f-semiperfect modules. We show that: (i) every generalized f-semiperfect module over a regular ring is f-semiperfect; (ii) for small or for finitely generated submodules L of M, the factor module M/L is generalized f-semiperfect; (iii) If M is a projective and generalized f-semiperfect module such that every Rad-supplement in M is a direct summand of M, then every direct summand of M is a generalized f-semiperfect module; (iv) If M = circle plus M-i is an element of I(i) is a locally Noetherian and duo module such that {M-i}(i is an element of I) is the family of generalized f-semiperfect modules, then M is a generalized f-semiperfect module.