In last decades, the connectedness of some varieties of the prime spectra of a commutative
ring is investigated by many authors. Falting's connectedness theorem asserts that in an …

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 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. 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 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 M be a left R-module. The set of all prime submodules of M is called the spectrum of M
and denoted by Spec (RM), and that of all prime ideals of R is denoted by Spec (R). For …

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 …

Proposition 5.2 (3) and its result Proposition 6.3 in the published version [1] are incorrect.
The original Proposition 5.2 (3) in [1] states: For a module M over a ring R, let P be an …

Let R be an associative ring with identity and Specs (M) denote the set of all second
submodules of a right R-module M. In this paper, we investigate some interrelations …