Properties of the subtractive prime spectrum of a semimodule

For a top semimodule over semiring with zero and nonzero identity, this paper studies the interplay between topological properties of subtractive prime spectrum algebraic semimodule. We prove that subtractively finitely generated is compact space, establish necessary sufficient conditions for to be generated. For
 multiplication commutative semiring, we radical subsemimodule coincides its radical, every proper contained in subsemimodule, iff spectrum, intersection many basic open sets compact, spectral space.