On ST-Essential (Complement)


Let R be an associative ring with identity and let D be a left R-module. As a generalization of T-essential we introduce the concept of the small T-essential . Let T be a proper of a module D. A N such that N T is small T-essential (ST-essential) and denoted by , if for each L of a module D, such that T, implies that . We also define ST-complement submodules and show the relationships between ST-essential and S-closed, ST-essential and S-singular, and ST-complement and ST-essential submodules. Some properties and theories about these concepts are also provided.