Spectra of semimodules. (Q2895935)

The authors define prime subsemimodules for a semimodule \(M\) over a semiring \(R\) and study some of their properties. A proper subsemimodule \(N\) is called strong, if for any \(x\) in \(N\) there exists a \(y\) in \(N\) such that \(x+y=0\). For strong subsemimodules and semiideals, mainly for a finitely generated semimodule, the authors establish some results. If \(S\) is a multiplicatively closed subset of the commutative semiring \(R\) and \(M\) is an \(R\)-semimodule, then a relationship between \(\text{Spec}(M)\) and \(\text{Spec}(M_S)\) is found. Then the notions of prime ideals and primary subsemimodules are also investigated.