(untitled) (European Journal of Pure and Applied Mathematics, 2018)
We have introduced the notion of α-prime and weakly α-prime submodules as a generalization of prime submodules. Some basic properties of α-prime and weakly α-prime submodules are the extension of prime submodules. Finally, after introducing the notion of α-prime submodules, we also define and study the concept of α-prime ideals in a ring.