In this paper, we study some properties of φ-prime submodules andwe give another charactrization for it. For given N and K a moduleM with ⊆ N, prove that is submodule if only N/Kis φ_K-prime submodule. Finally, show any finite sum isφ-prime.

By recent results of M. Stronkowski, it is known that not all modes embed as subreducts into semimodules over commutative unital semirings. Related to this problem is the problem of constructing a (commutative unital) semiring defining the variety of semimodules whose idempotent subreducts lie in a given variety of modes. We provide a general construction of such semirings, along with basic exa...