Weak Essential Submodules

A non-zero submodule N of M is called essential if N intersection L neq 0 for each nonzero submodule L of M. And a non-zero submodule K of M is called semi-essential if K intersection P neq 0 for each non-zero prime submodule P of M. In this paper we investigate a class of submodules that lies between essential submodules and semi-essential submodules, we call these class of submodules weak essential submodules.