Semi-Essential Submodules and Semi-Uniform Modules

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.