Results 11 to 20 of about 477 (118)
Formalized Mathematics, 2018 Summary We formalize in the Mizar system [3], [4] basic definitions of commutative ring theory such as prime spectrum, nilradical, Jacobson radical, local ring, and semi-local ring [5], [6], then formalize proofs of some related theorems along with the first chapter of [1]. The article introduces
Watase, Yasushige
openaire +4 more sources
Zariski topology on the spectrum of graded classical prime submodules [PDF]
Applied General Topology, 2013 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 every $a, b\in h(R)$, $m\in h(M)$, whenever $abm\in N$, then either $am\in N$ or $bm ...
Ahmad Yousefian Darani, Shahram Motmaen
doaj +2 more sources
A dual Zariski topology for modules
Topology and its Applications, 2011 We introduce a dual Zariski topology on the spectrum of fully coprime $R$-submodules of a given duo module $M$ over an associative (not necessarily commutative) ring $R$. This topology is defined in a way dual to that of defining the Zariski topology on the prime spectrum of $R$.
Abuhlail, Jawad, Jawad Abuhlail
openaire +3 more sources
The Markov–Zariski topology of an abelian group
Journal of Algebra, 2010 According to Markov, a subset of an abelian group G of the form {x in G: nx=a}, for some integer n and some element a of G, is an elementary algebraic set; finite unions of elementary algebraic sets are called algebraic sets. We prove that a subset of an abelian group G is algebraic if and only if it is closed in every precompact (=totally bounded ...
DIKRANJAN, Dikran, SHAKHMATOV D.
openaire +4 more sources
On the Zariski topology over an $L$-module $M$
TURKISH JOURNAL OF MATHEMATICS, 2017 Summary: Let \(L\) be a multiplicative lattice and \(M\) be an \(L\)-module. In this study, we present a topology said to be the Zariski topology over \(\sigma (M)\), the collection of all prime elements of an \(L\)-module \(M\). We research some results on the Zariski topology over \(\sigma (M)\). We show that the topology is a \(T_{0}\)-space and a \(
Çallıalp, Fethi +2 more
core +5 more sources
Modules and the second classical Zariski topology
Le Matematiche, 2018 The second author was supported by the Scientific Research Project Administration of Akdeniz University.
Ceken, Secil, Alkan, Mustafa
core +5 more sources
On A Subspace Of Dual Zariski Topology On A Subspace Of Dual Zariski Topology
AIP Conference Proceedings, 2017 Let R be a commutative ring with identity and S pee (M) (resp. Min(M)) denote the set of all second (resp minimal) submodules of a non-zero R-module M. In this paper, we investigate several properties of the subspace topology on Min(M) induced by the dual Zariski on S pee(M) and determine some cases in which Min(M) is a max-spectral space.
Ceken, Secil, Seçil Çeken
openaire +3 more sources
On the upper dual Zariski topology
Filomat, 2020 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 second submodule Q of M is called an upper second submodule if there exists a prime ideal p of R such that
Ceken, Secil
openaire +4 more sources
Zariski topology on the secondary-like spectrum of a module
Open Mathematics, 2022 Let ℜ\Re be a commutative ring with unity and ℑ\Im be a left ℜ\Re -module. We define the secondary-like spectrum of ℑ\Im to be the set of all secondary submodules KK of ℑ\Im such that the annihilator of the socle of KK is the radical of the ...
Salam Saif, Al-Zoubi Khaldoun
doaj +3 more sources
Formal Zariski topology: Positivity and points
Annals of Pure and Applied Logic, 2006 In the context of formal (pointfree) topology, i.e. predicative locale theory, the author considers the Zariski spectrum of a commutative ring. We recall that the Zariski spectrum is a solution to the following universal problem: for each commutative ring \(A\) with unit, find a topological space and a sheaf of local rings on it such that \(A\) is the ...
Peter Schuster, Schuster, Peter
openaire +3 more sources