Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …

Let R be a commutative ring with identity and let M be an R-module. A proper submodule P
of M is called a classical prime submodule if abm Î P for a, b Î R, and m Î M, implies that am Π…

Let R be a commutative ring with identity and let M be an R-module. A proper submodule P
of M is called a classical prime submodule if abm∈ P for a, b∈ R, and m∈ M, implies that …

Let R be a ring, M be a left R-module and Spec (RM) be the collection of all prime
submodules of M. In this paper and its sequel, we introduce and study a generalization of …

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 R be a commutative ring and let M be an R-module. Let X= Spec (M) be the prime
spectrum of M with Zariski topology. Our main purpose in this paper is to specify the …

Let M be a non-zero module over an associative (not necessarily commutative) ring. In this
paper, we investigate the so-called second and coprime submodules of M. Moreover, we …

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 …

In this paper we continue our study of classical Zariski topology of modules, that was
introduced in Part I (see [2]). For a left R-module M, the prime spectrum Spec (RM) of M is …

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 …