Spectral spaces are a class of topological spaces. They are a tool linking algebraic
structures, in a very wide sense, with geometry. They were invented to give a functional …

Let R be a commutative ring and M be an R-module. The second spectrum Spec s (M) of M
is the collection of all second submodules of M. We topologize Spec s (M) with Zariski …

We establish conditions for Spec (M) to be Noetherian and spectral space, wrt different
topologies. We used rings with Noetherian spectrum to produce plentiful examples of …

Let R be a commutative ring and M an R-module. Let Spec^ s (M) S pecs (M) be the
collection of all second submodules of M. In this article, we consider a new topology on …

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-
module. A proper graded submodule N of M is called a graded classical prime if whenever r …

The subject of this paper is the Zariski topology on a multiplication module $ M $ over a
commutative ring $ R $. We find a characterization for the radical submodule $ rad_ {M}(0) …

Full article: Prime Submodules and a Sheaf on the Prime Spectra of Modules Skip to Main
Content Taylor and Francis Online homepage Taylor and Francis Online homepage Log in …

Let $ R $ be a commutative ring and let $ M $ be an $ R $-module. In this article, we
introduce the concept of the Zariski socles of submodules of $ M $ and investigate their …

Let R be a commutative ring with identity and Spec^ s (M) Spec s (M) denote the set all
second submodules of an R-module M. In this paper, we investigate various properties of …

Let R be a commutative ring having nonzero identity and M be a unital R-module. Assume
that S⊆ R is a multiplicatively closed subset of R. Then, M satisfies S-Noetherian spectrum …