Let R be a commutative semiring with identity and M be a unitary R-semimodule. Let φ : S(M) → S(M) ∪ {∅} be a function, where S(M) is the set of all subsemimodules of M. A proper subsemimodule N of M is called φ-primary subsemimodule, if whenever r ∈ R and x ∈ M with rx ∈ N − φ(N), implies that r ∈ p (N :R M) or x ∈ N. So if we take φ(N) = ∅ (resp., φ(N) = {0}), a φ-primary subsemimodule is primary (resp., weakly primary). In this paper, we study the concept of φ-primary subsemimodule which is a generalization of φ-prime subsemimodule in a commutative semiring.
