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View article: Zero Intersection Graph of Annihilator Ideals of Modules
Zero Intersection Graph of Annihilator Ideals of Modules Open
This paper aims to associate a new graph to nonzero unital modules over commutative rings. Let R be a commutative ring having a nonzero identity and M be a nonzero unital R-module. The zero intersection graph of annihilator ideals of R-mod…
View article: On generalized morphic modules
On generalized morphic modules Open
Aim of the present article is to extend generalized morphic ring to modules. Let R be a commutative ring with a unity and M an R -module. M is said to be a generalized morphic module if for each m ∈ M , there exists a ∈ R such that ann R (…
View article: On normal modules
On normal modules Open
Recall that a commutative ring R is said to be a normal ring if it is reduced and every two distinct minimal prime ideals are comaximal. A finitely generated reduced R-module M is said to be a normal module if every two distinct minimal pr…
View article: Generalizations of strongly hollow ideals and a corresponding topology
Generalizations of strongly hollow ideals and a corresponding topology Open
In this paper, we introduce and study the notions of $ M $-strongly hollow and $ M $-PS-hollow ideals where $ M $ is a module over a commutative ring $ R $. These notions are generalizations of strongly hollow ideals. We investigate some p…
View article: On the upper dual Zariski topology
On the upper dual Zariski topology Open
Let R be a ring with identity and M be a left R-module. The set of all second submodules of M is called the second spectrum of M and denoted by Specs(M). For each prime ideal p of R we define Specsp(M) := {S? Specs(M) : annR(S) = p}. A sec…
View article: A sheaf on the second spectrum of a module
A sheaf on the second spectrum of a module Open
Let R be a commutative ring with identity and Specs(M) denote the set all second submodules of an R-module M. In this paper, we construct and study a sheaf of modules, denoted by O(N; M), on Specs(M) equipped with the dual Zariski topology…
View article: Modules and the Second Classical Zariski Topology
Modules and the Second Classical Zariski Topology Open
Let R be an associative ring with identity and Spec^{s}(M) denote the set of all second submodules of a right R-module M. In this paper, we present a number of new results for the second classical Zariski topology on Spec^{s}(M) for a righ…
View article: On the weakly second spectrum of a module
On the weakly second spectrum of a module Open
In this paper, we extend the definition of weakly second submodule of a module over a commutative ring to a module over an arbitrary ring. First, we investigate some properties of weakly second submodules. We define the notion of weakly se…
View article: Invariant theory for quantum Weyl algebras under finite group action
Invariant theory for quantum Weyl algebras under finite group action Open
We study the invariant theory of a class of quantum Weyl algebras under group actions and prove that the fixed subrings are always Gorenstein. We also verify the Tits alternative for the automorphism groups of these quantum Weyl algebras.