ᴪ-Prime Submodules

Let R be a commutative ring with identity and M be an unitary R-module. Let (M) be the set of all submodules of M, and ᴪ: (M) - (M) υ {ф} be a function. We say that a proper submodule P of M is £-prime if for each r £ R and x ᴪ M, if rx £ P, then either x £ P + ᴪ(P) or r M c P + ᴪ(P) . Some of the properties of this concept will be investigated. Some characterizations of ᴪ-prime submodules will be given, and we show that under some assumptions prime submodules and ᴪ-prime submodules are coincide.