Weakly Nearly Primary Submodules

The concept of weakly nearly primary submodule in this paper is a new generalization of weakly prime submodule. Several basic properties and examples of this concept were established. Furthermore, many characterizations of weakly nearly primary submodules are given. Moreover, we show that by example the residual of a weakly nearly primary submodule need not be a weakly nearly primary ideal, but the converse holds under sufficient conditions. Finally, in this paper, we stand for a commutative ring with identity and is a unitary left -module.