Let 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 r 2 R and x 2 M with rx 2 N nϕ(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 generalizations of prime subsemimodules.
