Results 11 to 20 of about 16,887 (181)
Spectrum of Zariski Topology in Multiplication Krasner Hypermodules
Mathematics, 2023 In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings.
Ergül Türkmen +2 more
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Topologizable structures and Zariski topology [PDF]
Algebra universalis, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dutka, Joanna, Ivanov, Aleksander
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A Zariski Topology for Bicomodules and Corings [PDF]
Applied Categorical Structures, 2007 In this paper we introduce and investigate top (bi)comodules} of corings, that can be considered as dual to top (bi)modules of rings. The fully coprime spectra of such (bi)comodules attains a Zariski topology, defined in a way dual to that of defining the Zariski topology on the prime spectra of (commutative rings.
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A Zariski Topology for Modules [PDF]
Communications in Algebra, 2011 Given a duo module $M$ over an associative (not necessarily commutative) ring $R,$ a Zariski topology is defined on the spectrum $\mathrm{Spec}^{\mathrm{fp}}(M)$ of {\it fully prime} $R$-submodules of $M$. We investigate, in particular, the interplay between the properties of this space and the algebraic properties of the module under consideration.
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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.
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S-Zariski topology on S-spectrum of modules
Filomat, 2022 Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, first we give some relations between S-prime and S-maximal submodules that are generalizations of prime and maximal submodules, respectively. Then we construct a topology on the set of all S-prime submodules of M , which is generalization of prime ...
Ersoy, Bayram Ali +2 more
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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 $R$.
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Zariski topology on the secondary-like spectrum of a module
Open MathematicsLet 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
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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
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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
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