Z- Essentail Small Compressible Modules

Mustafa M. Hameed; Alaa A.  Elewi

doi:10.30526/39.3.4325

Authors

Mustafa M. Hameed Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0002-8627-4581
Alaa A. Elewi Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0002-8627-4581

DOI:

https://doi.org/10.30526/39.3.4325

Keywords:

Z-small sub-module, Z- essential small sub-module, compressible module, Z- essential small compressible module

Abstract

Let C be the left unitary R-module , and let R be a commutative ring with 1. In this paper, we introduce a detail and study the concept of a Z- essential small compressible module (Z-ess-s-comp module for short), if C can be embedded in each of its non-zero Z-small sub-module. Equivalently, C is a Z-ess-s-comp module if there exists a monomorphism from C into N whenever 0≠N≪_(z-ess) C, as a generalization of the compressible module (comp module for short), and gives some of their properties, characterizations, and examples. On the other hand, we study the relations between Z-ess-s-compressible modules and some classes of modules. We also presented the two concepts of Z-essentail small prime (module, submodule) Z-essential small uniform module (where C is called a Z-essentail small uniform module if any non-zero Z-essential small sub-module of C is essential. and provide the relationships between Z-ess-s-compressible modules, Z-essentail small prime module, and Z-essential small uniform module

Author Biographies

Mustafa M. Hameed, Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq

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Alaa A. Elewi , Department of Mathematics, College of Sciences, University of Baghdad, Baghdad, Iraq

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