Generalized f-semiperfect Modules - Türkmen, Burcu Nişancı; Pancar, Ali (Communications in Mathematics and Applications, 2013)
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 ML 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=_iIM_i is a locally Noetherian and duo module such that {M_i}_iI is the family of generalized f-semiperfect modules, then M is a generalized f-semiperfect module.