Ѱ-prime submodules

Abstract EN

Let R be a commutative ring with identity and M be an unitary R-module.

Let 6(M) be the set of all submodules of M, and y: 6(M)-> 6(M) u {(^} be a function.

We say that a proper submodule P of M is y-prime if for each r e R and x e M, if rx e P, then either x e P + y(P) or r M c P + y(P) .

Some of the properties of this concept will be investigated.

Some characterizations of y-prime submodules will be given, and we show that under some assumptions prime submodules and y-prime submodules are coincide.