On alpha-prime and Weakly alpha-prime Submodules

Abstract

We have introduced the notion of $\alpha$-prime and weakly $\alpha$-prime submodules as a generalization of prime submodules. Some basic properties of $\alpha$-prime and weakly $\alpha$-prime submodules are the extension of prime submodules. Finally, after introducing the notion of $\alpha$-prime submodules, we also define and study the concept of $\alpha$-prime ideals in a ring.