Some Properties of Prime Submodules and the Effect of Localization on Their Structures
Maximal submodules
prime submodules
gw-prime submodules
multiplicative systems
localization
In this paper, prime modules are studied and investigated. Some properties of this type of submodules are proved. Some conditions are given under which every submodule of a prime submodule is maximal and some conditions are given which make every proper submodule of prime modules as a prime submodule. It is proved that multiplication modules in which prime submodules are finitely generated are Noetherian. In addition, the effects of localization on prime submodules are studied and some results concerning the localization of prime submodules are proved.