Let R be a commutative semiring with identity and M be a unitary R-semimodule. Let be a function, where is the set of all subsemimodules of M. A proper subsemimodule N of M is called φ-prime subsemimodule, if r ∈ R and x ∈ M with rx ∈ N \ φ(N) implies that r ∈ (N :_RM) or x ∈ N. So if we take φ(N) = ∅︀ (resp., φ(N) = {0}), a φ-prime subsemimodule is prime (resp., weakly prime). In this article we study the properties of several generalizations of prime subsemimodules.

Keywords: prime subsemimodule, weakly prime subsemimodule, ϕ-prime subsemimodule