Generalized F-Semiperfect Modules

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.