In previous research, a concept was presented f–small submodules A submodule L of an R-
module W is named f–small if L+ X= W and W/X are small-singular, then X= W. In this work …

The goal of this research is to introduce the concepts of Large-small submodule and Large-
hollow module and some properties of them are considered, such that a proper submodule …

In this sheet, we give a definition" Essential β-hollow module (Eβ-HM) and Essential β-lifting
module (Eβ-LM)". A module M is named Essential β-hollow module (Eβ-HM), if∀ X≤ M …

In our previous work, we submitted a concept about small-singular submodules. In this
paper, we create a new concept, namely f-small submodules, this concept is an extension of …

Hollow module, which is an important concept is studied in this article. The main property
about this module is a cyclic module with radical it means M is hollow module. On the other …

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 …

In this paper, we introduce hollow modules with respect to an arbitrary submodule. Let M be
a non-zero module and T be a submodule of M. We say that M is aT-hollow module if every …

The main goal of this paper is to give a new generalizations for two important classes in the
category of modules, namely the class of small submodules and the class of hollow …

In this work, FZ-hollow and Z-semihollow modules are defined as a generalization of F-
hollow and semihollow modules, and some properties of these concepts of modules are …

A submodule Ϝ of an R-module Ε is called small in Ε if whenever, for some submodule W of
Ε, implies. In this paper, we introduce the notion of Ζ-small submodule, where a proper …