Spectra of semimodules

The purpose of this paper is to investigate possible structures and useful properties of prime subsemimodules of a semimodule $M$ over a semiring $R$ and show various applications of the properties. The main part of this work is to introduce a new class of semimodules over $R$ called strong primeful $R$-semimodules. It is shown that every non-zero strong primeful semimodule possesses the non-empty prime spectrum with the surjective natural map. Also, it is proved that this class contains the family of finitely generated $R$-semimodules properly.