The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
Let
Let R be a ring with identity and M is a unitary left R–module. M is called J–lifting module if for every submodule N of M, there exists a submodule K of N such that
In this paper, we introduce the concepts of Large-lifting and Large-supplemented modules as a generalization of lifting and supplemented modules. We also give some results and properties of this new kind of modules.