et R be a commutative semiring with identity and M be a unitary R-semimodule. Let φ : S(M) ! S(M) [ f;g be a function, where S(M) is the set of all subsemimodules of M. A proper subsemimodule N of M is called φ-prime subsemimodule, if whenever r 2 R and x 2 M with rx 2 N − φ(N), implies that r 2 (N :R M) or x 2 N. So if we take φ(N) = ; (resp., φ(N) = f0g), a φ-prime subsemimodule is prime (resp., weakly prime). In this article we study the properties of several generalization of prime subsemimodules.
