On modules satisfying \(S\)-Noetherian spectrum condition (Q6169188)

In this article, the focus is on modules satisfying the \(S\)-Noetherian spectrum condition. The authors define this condition for a commutative ring with a multiplicatively closed subset and a module. They provide properties and characterizations of modules satisfying this condition and prove a result analogous to Cohen's theorem. They also characterize modules with a Noetherian spectrum in terms of modules satisfying the \(S\)-Noetherian spectrum condition.