End-Ѱ-prime submodules

Abstract EN

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

Let 5(M) be the set of all submodules of M, and y: 5(M)-> 5(M) u be a function.

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

Some of the properties of this concept will be investigated.

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