Compressible Modules

The main purpose of this paper is to study under what condition compressible modules are critically compressible. A sufficient condition for the injective hull of a critically compressible module to be critically compressible is also provided. Furthermore we prove sufficient conditions for a critically compressible module to be continuous. In addition, some characterization of critically compressible modules in terms of CS modules, nonsingular modules and cyclic modules are also provided