Semi-Essential Submodules and Semi-Uniform Modules

Mijbass, Ali S.; Abdullah, Nada K.

doi:10.32894/kujss.2009.40796

Semi-Essential Submodules and Semi-Uniform Modules

Document Type : Research Paper

Authors

Ali S. Mijbass ¹
Nada K. Abdullah ²

¹ Science college-Tikrit University

² Education College-Tikrit University

10.32894/kujss.2009.40796

Abstract

In this work,we give generalizations for the concepts essential submodule and uniform module.We call an R-submodule N of M semi-essential if N∩P≠0 for each nonzero prime R- submodule P of M, and we call an R- module M semi - uniform if every nonzero R-submodule N of M is semi-essential. Moreover, we generalize some properties of essential R-submodules to semi-essential R-submodules,and we generalize some properties of uniform R-modules to semi-uniform R-module. We also give conditions under them an R-submodule N of a multiplication R- module M becomes semi- essential. Furthermore, we give some conditions under them an R-module M satisfies ACC(DCC) on semi-essential R-submodules.

Keywords