Semi-Essential Submodules and Semi-Uniform Modules
Kirkuk University Journal-Scientific Studies,
2009, Volume 4, Issue 1, Pages 48-58
AbstractIn 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.
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