Results 11 to 20 of about 2,589 (113)
Zariski Subspace Topologies On Ideals
Hacettepe Journal of Mathematics and Statistics, 2018 Summary: In this paper, we show how there are tight relationships between algebraic properties of a commutative ring \(R\) and topological properties of open subsets of Zariski topology on the prime spectrum of \(R\). We investigate some algebraic conditions for open subsets of Zariski topology to become quasi-compact, dense and irreducible.
ÖNEŞ, Ortaç, ALKAN, Mustafa
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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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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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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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Symbolic powers of ideals [PDF]
, 2017 We survey classical and recent results on symbolic powers of ideals. We focus on properties and problems of symbolic powers over regular rings, on the comparison of symbolic and regular powers, and on the combinatorics of the symbolic powers of monomial ...
Dao, Hailong +4 more
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The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring [PDF]
, 2007 Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to the well known patch or constructible topology.
Fontana, Marco, Loper, K. Alan
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The Zariski Topology for distributive lattices
Rocky Mountain Journal of Mathematics, 1987 The purpose of this paper is to study an intrinsic topology for distributive lattices which by its very definition is analogous to the classical Zariski topology on rings. As in the case of rings, the Zariski topology is the coarsest topology making solution sets of polynomials closed.
Gierz, Gerhard, Stralka, Albert
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Quasi-prime Submodules and Developed Zariski Topology [PDF]
Algebra Colloquium, 2012 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 investigate the relationship between algebraic properties of M and topological properties of q Spec (M).
Abbasi, A., Hassanzadeh-lelekaami, D.
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Inverse topology in BL-algebras
پژوهشهای ریاضی, 2020 In this paper, we introduce Inverse topology in a BL-algebra A and prove the set of all minimal prime filters of A, namely Min(A) with the Inverse topology is a compact space, Hausdorff, T0 and T1-Space.
Fereshteh Forouzesh +2 more
doaj
Zariski‐type topology for implication algebras
Mathematical Logic Quarterly, 2010 AbstractIn this work we provide a new topological representation for implication algebras in such a way that its one‐point compactification is the topological space given in [1]. Some applications are given thereof (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Abad, Manuel +2 more
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