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 with identity, and let M be an R-module. There are different
Zariski topologies defined on the prime spectrum Spec (M). In this article, we will determine …

Let M be a module over a commutative ring, and let Spec (M) be the collection of all prime
submodules of M. We topologize Spec (M) with Zariski topology, which is analogous to that …

Let $ L $ be a multiplicative lattice and $ M $ be an $ L $-module. In this study, we present a
topology said to be the Zariski topology over $\sigma (M), $ the collection of all prime …

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 …

For any module M over a commutative ring R, Spec_ R (M) S pec R (M)(resp. Max_ R (M) M
ax R (M)) of M is the collection of all prime (resp. maximal) submodules. In this article, we …

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 and let M be a top R-module. In this article, we investigate some
properties of a new class of modules, called strongly top modules. Studying of this family …

Let R be a commutative ring with identity and M be a unital R-module. The primary-like
spectrum SpecL (M) is the collection of all primary-like submodules Q of M such that M/Q is a …

For a module M over a commutative ring R with identity, let RSpec (M) denote the collection
of all submodules L of Msuch that√(L: M) is a prime ideal of R and is equal to (rad L: M). In …