Purely Small Submodules and Purely Hollow Modules

Muna Abbas Ahmed; Iman Abdulhadi Dhari; Zainab Abed Atiya

doi:10.24996/ijs.2022.63.12.34

Authors

Muna Abbas Ahmed Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad,
Iman Abdulhadi Dhari Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad,
Zainab Abed Atiya Department of Mathematics, College of Science for Women, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.12.34

Keywords:

Pure submodules, Purely small submodules, Purely hollow modules

Abstract

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 modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of purely hollow modules is considered.