On C. lifting and Semi*perfect Modules

In this paper, we introduce c. lifting module as a generalization of lifting module, we prove some results on c. lifting module, also we introduce semi*perfect module as a generalization of a semiperfect module and direct summand generalized* co-finitely weakly supplemented module as a generalization of a direct summand co-finitely weakly supplemented module and we prove under certain conditions c. lifting, semi*perfect and direct summand generalized* co- finitely weakly supplemented modules are equivalent. Keywords:lifting modules,co-finitely semiperfect modules, direct summand supplemented modules, generalization of lifting modules and generalization of a generalized weakly supplemented modules

A generalization of supplemented modules

Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is an analogous of δ-supplemented modules defined by Kosan. The module M is called principally δ-supplemented, for all m∈M there exists a submodule A of M with M=mR+A and (mR)∩A δ-small in A. We prove that some results of δ-supplemented modules can be extended to principally δ-supplemented modules for this general settings. We supply some examples showing that there are principally δ-supplemented modules but not δ-supplemented. We also introduce principally δ-semiperfect modules as a generalization of δ-semiperfect modules and investigate their properties

Modul Bersuplemen Utama Sebagai Generalisasi Dari Modul Bersuplemen

An R-module M is called supplemented if every submodule of M has a supplement in M. Principally supplemented modules are defined as generalizations of lifting, principally lifting and supplemented modules. In this paper, we will characterize principally supplemented modules as a generalization of supplemented module respect to duo module and distributive module

A generalization of g-supplemented modules

In this work g-radical supplemented modules are defined which generalize g-supplemented modules. Some properties of g-radical supplemented modules are investigated. It is proved that the finite sum of g-radical supplemented modules is g-radical supplemented. It is also proved that every factor module and every homomorphic image of a g-radical supplemented module is g-radical supplemented. Let R be a ring. Then R-R is g-radical supplemented if and only if every finitely generated R-module is g-radical supplemented. In the end of this work, it is given two examples for g-radical supplemented modules separating with g-supplemented modules