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 …

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 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 …

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 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 an R-module. The purpose of this article is to introduce a
new class of modules over R called X-injective R-modules, where X is the prime spectrum of …

The Zariski Topology on the Prime Spectrum of a Module over Noncommutative Rings Page 1
Algebra Colloquium c© 2009 AMSS CAS & SUZHOU UNIV Algebra Colloquium 16 : 4 (2009) …

Given a duo module M over an associative (not necessarily commutative) ring R, a Zariski
topology is defined on the spectrum Specfp (M) of fully prime R-submodules of M. We …