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 …

Let; M be a unitary; left R-module on; associative ring with; identity; R. A submodule; K of M
is called; R-ann-small; if K+ T= M, where T is a submodule of M, implies that ann (T)= 0 …

A module M is called generalized extending if for any submodule N of M, there is a direct
summand K of M such that N≤ K and K/N is singular. Any extending module and any …

Let R be a commutative ring with unity and M be a non zero unitary left R-module. M is
called a hollow module if every proper submodule N of M is small (N≪ M), ie N+ W≠ M 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 …

To consider R is a commutative ring with unity, be a nonzero unitary left R-module, is known
hollow module if each proper submodule of is small. L-hollow module is a strong form of …

The purpose of this paper is to introduce new concepts in a module over a ring, the first one
is called e*-small essential submodule, which is a generalization of the small submodule …

Let R be an associative ring with identity and let M be right R-module M is called μ-semi
hollow module if every finitely generated submodule of M is μ-small submodule of M The …

⊕-supplemented modules as a famous generalization of lifting (projective supplemented)
modules were widely studied in the last decades. In this paper, we peruse a homological …