Strong Essential Submodules And Strong Uniform Modules

Abstract

A non-zero submodule K of an R-module M is called essential if K  L  (0)  for each non-zero submodule L of M . And an R-module M is called uniform if each non-zero submodule of M is an essential . In this paper we give generalization of essential submodule and uniform module that are strong essential submodule and strong uniform module. A non-zero submodule N of M is called strong essential if  N  P  (0) for each non-zero strongly prime submodule P of M . And an R-module M is called strong uniform if each non-zero submodule of M is a strong essential .