We focus on some notions of prime submodules over a commutative ring with identity. Suppose R is a commutative ring with identity and M is an R-module. For more generalized version of prime module, we have weakly and almost prime submodules by defining different sets that contain the multiplication between element of ring and element of module. Furthermore, by using concept of the module localization, we have a definition of a strongly prime submodule. A fully prime module is a module in which every proper submodule is a prime submodule. Also, we show that if M is a torsion-free fully prime module over integral domain R, then every quotient of a strongly prime submodule M is strongly prime. Several characterizations of an almost prime submodule are obtained.

almost prime submodule, module localization, strongly prime submodule, fully prime submodule, prime submodules.