Let R be a ring with identity and let $ M= M_1 {\bigoplus} M_2 $ be an amply supplemented
R-module. Then it is proved that $ M_i $ has ($ D_1 $) and is $ M_j-^* ojective $ for $ i {\neq} …

Let R be a ring with identity and let M be a left R-module. M is called µ-lifting modulei f for
every sub module A of M, There exists a direct summand D of M such that M= D⊕ D', for …

Keskin and Harmanci defined the family B (M, X)= ${A {\leq} M|{\exists} Y {\leq} X,{\exists} f
{\in} Hom_R (M, X/Y),\; Ker\; f/A {\ll} M/A} $. And Orhan and Keskin generalized projective …

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …

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 analogous to that of Goldie*-lifting and principally Goldie*-lifting …

In this note, we introduce the (small, pseudo-) ℬ (M, X)-cojective modules and we generalize
(small, pseudo-) cojective modules via the class ℬ (M, X). Let M= M1⊕ M2 be an X-amply …

Harada (cf.) introduced the lifting property for maximal submodules and the extending
property for simple submodules, and Oshiro (cf.) definitely introduced lifting modules and …

Lifting modules as a main concept in module theory have been studied and investigated
extensively in recent decades. The first author in [1] tried to consider and investigate this …

In this paper, we study a module which is lifting and supplemented relative to a module
class. Let R be a ring, and let X be a class of R-modules. We will define X-lifting modules …

An R-module M is called an extending module, and also called CS, if it satisfies the following
full extending property: For any submodule X of M, there exists a direct summand X∗ of M …