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To consider R is a commutative ring with unity,  be a nonzero unitary left   R-module,  is known hollow module if each proper submodule of  is small.  L-hollow module is a strong form of hollow module, where an R-module  is known L-hollow module if  has a unique maximal submodule which contains each small submodules. The current study deals with this class of modules and give several fundamental properties  related with this concept.

Amodule M is called comp. Hopfian if any epomorphism f  End (M) . ker f is complement of N in M for some submodule N of M . In this study, some properties of comp. Hopfian modules are investigated with examples .

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 .