Z-Small Quasi-Dedekind Modules

Farhan Dakhil Shyaa; Hawraa Abd Al-Sada

doi:10.24996/ijs.2023.64.6.26

Authors

Farhan Dakhil Shyaa Department of Mathematics, College of Education, University of Al-Qadsiyah, Al-Qadsiyah, Iraq https://orcid.org/0000-0003-1123-1974
Hawraa Abd Al-Sada Department of Mathematics, College of Education, University of Al-Qadsiyah, Al-Qadsiyah, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.6.26

Keywords:

Quasi-Dedekind module, Z-small quasi-Dedekind module, Second singular submodule

Abstract

In this paper, we define and study z-small quasi-Dedekind as a generalization of small quasi-Dedekind modules. A submodule of -module is called z-small ( if whenever , then . Also, is called a z-small quasi-Dedekind module if for all implies . We also describe some of their properties and characterizations. Finally, some examples are given.