Small Prime Modules and Small Prime Submodules

Let R be a commutative ring with identity, and M be a unital (left) R-module. In this paper we introduce and study the concepts: small prime submodules and small prime modules as generalizations of prime submodules and prime modules. Among the results that we obtain is the following: An R-module M is small prime if and only if the R-module R/annM is cogenerated by every non-trivial small submodule of M.