Extending modules are generalizations of injective modules and, dually, lifting modules
generalize projective supplemented modules. There is a certain asymmetry in this duality …

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 …

In this study, it is investigated the relation between almost projective modules and
generalized projective modules. These concepts are useful for the study on finite direct sum …

In this note, we investigate the relationship between almost projective modules and
generalized projective modules. These concepts are useful for the study on the finite direct …

Let M and X be R-modules. We define the X--supplemented modules via the class  B
(M, X) as a generalization of-supplemented modules. We show that any finite direct sum …

Let M and X be right R-modules. We introduce several modules relative to the class of B (M,
X) and we investigate relation among these modules. In this note, we show if M is X …

Let M be a right R-module. M is called XH-supplemented if for every submodule A of M with
A∈ B (M, X) there exists a direct summand D of M such that M= A+ Y if and only if M= D+ Y …

Polynomials can be used to describe almost any problem from a lot of practical problems in
robotics, computer vision, computational biology, solid modelling, mechanical and chemical …

In this paper we introduce the (∗)-generalized projective modules as a proper
generalization of projective modules. We also investigate the” When is direct sum of two …

Proof.(a)⇒(b). If M= X⊕ X and U/X≪ M/X, then U= X+(U∩ X). Let φ: M/X→ X be the obvious
isomorphism. Then, since U/X≪ M/X, we have (U/X) φ= U∩ X≪ X. Hence U∩ X≪ …