Let $ R $ be a $ G $-graded commutative ring with identity and let $ M $ be a graded $ R $-
module. A proper graded submodule $ N $ of $ M $ is called graded classical prime if for …

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 …

Let R be a G-graded commutative ring with identity and let M be a graded R-module. We
endow Specg (M), the collection of all graded prime submodules of M, analogous to that for …

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-
module. In this paper, we introduce and study a new topology on Cl. Specg (M), the …

Let G be a group with identity e and let R be a G-graded ring. A proper graded ideal P of R is
called a graded primary ideal if whenever rgsh∈ P, we have rg∈ P or sh∈ Gr (P), where rg …

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 …

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) …

Let R be a commutative ring with nonzero identity and M be an R-module. Quasi-prime
submodules of M and the developed Zariski topology on q Spec (M) are introduced. We also …

Throughout this paper, all rings are associative rings with an identity and all modules are
unitary right R-modules. Let M be a right R-module and S= End R (M), its endomorphism …