Relevant bibliographies by topics / Zariski topology

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  2. Dissertations / Theses
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  5. Conference papers

Academic literature on the topic 'Zariski topology'

Author: Grafiati
Published: 6 September 2023
Last updated: 25 July 2025

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Journal articles on the topic "Zariski topology"

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Watase, Yasushige. "Zariski Topology." Formalized Mathematics 26, no. 4 (2018): 277–83. http://dx.doi.org/10.2478/forma-2018-0024.

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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 the so-called Zariski topology. The set of all prime ideals of a commutative ring A is called the prime spectrum of A denoted by Spectrum A. A new functor Spec generates Zariski topology to make Spectrum A a topological space. A different role is given to Spec as a map from a ring morphism of commutat
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Mustafa, Hadi J., and Ameer Mohammad-Husain Hassan. "Near Prime Spectrum." Journal of Kufa for Mathematics and Computer 1, no. 8 (2013): 58–70. http://dx.doi.org/10.31642/jokmc/2018/010808.

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Let  be a commutative ring with identity . It is well known that a topology was defined for  called the Zariski topology (prime spectrum) . In this paper we will generalize this idea for near prime ideal . If  be a commutative near-ring with identity ,  be a near prime ideal of  and define  . Then  can be endowed with a topology similar to the Zariski topology which is called near Zariski topology (near prime spectrum) . we studies and discuss some of properties of such topology .
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Hassanzadeh-Lelekaami, Dawood, and Maryam Karimi. "Developed Zariski topology-graph." Discussiones Mathematicae - General Algebra and Applications 37, no. 2 (2017): 233. http://dx.doi.org/10.7151/dmgaa.1272.

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Rinaldi, Davide, Giovanni Sambin, and Peter Schuster. "The Basic Zariski Topology." Confluentes Mathematici 7, no. 1 (2016): 55–81. http://dx.doi.org/10.5802/cml.18.

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Dikranjan, Dikran, and Daniele Toller. "Zariski topology and Markov topology on groups." Topology and its Applications 241 (June 2018): 115–44. http://dx.doi.org/10.1016/j.topol.2018.03.025.

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JUNKER, MARKUS, and DANIEL LASCAR. "THE INDISCERNIBLE TOPOLOGY: A MOCK ZARISKI TOPOLOGY." Journal of Mathematical Logic 01, no. 01 (2001): 99–124. http://dx.doi.org/10.1142/s0219061301000041.

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We associate with every first order structure [Formula: see text] a family of invariant, locally Noetherian topologies (one topology on each Mn). The structure is almost determined by the topologies, and properties of the structure are reflected by topological properties. We study these topologies in particular for stable structures. In nice cases, we get a behaviour similar to the Zariski topology in algebraically closed fields.
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GOODEARL, K. R., and E. S. LETZTER. "THE CLOSED-POINT ZARISKI TOPOLOGY FOR IRREDUCIBLE REPRESENTATIONS." Journal of Algebra and Its Applications 05, no. 06 (2006): 719–30. http://dx.doi.org/10.1142/s0219498806001922.

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In previous work, the second author introduced a topology, for spaces of irreducible representations, that reduces to the classical Zariski topology over commutative rings but provides a proper refinement in various noncommutative settings. In this paper, a concise and elementary description of this refined Zariski topology is presented, under certain hypotheses, for the space of simple left modules over a ring R. Namely, if R is left noetherian (or satisfies the ascending chain condition for semiprimitive ideals), and if R is either a countable dimensional algebra (over a field) or a ring who
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Ballal, Sachin, and Vilas Kharat. "Zariski topology on lattice modules." Asian-European Journal of Mathematics 08, no. 04 (2015): 1550066. http://dx.doi.org/10.1142/s1793557115500667.

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Let [Formula: see text] be a lattice module over a [Formula: see text]-lattice [Formula: see text] and [Formula: see text] be the set of all prime elements in lattice modules [Formula: see text]. In this paper, we study the generalization of the Zariski topology of multiplicative lattices [N. K. Thakare, C. S. Manjarekar and S. Maeda, Abstract spectral theory II: Minimal characters and minimal spectrums of multiplicative lattices, Acta Sci. Math. 52 (1988) 53–67; N. K. Thakare and C. S. Manjarekar, Abstract spectral theory: Multiplicative lattices in which every character is contained in a uni
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Abuhlail, Jawad. "A Zariski Topology for Modules." Communications in Algebra 39, no. 11 (2011): 4163–82. http://dx.doi.org/10.1080/00927872.2010.519748.

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Xie, Junyi. "The existence of Zariski dense orbits for endomorphisms of projective surfaces." Journal of the American Mathematical Society 38, no. 1 (2022): 1–62. http://dx.doi.org/10.1090/jams/1004.

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Let f f be a dominant endomorphism of a smooth projective surface X X over an algebraically closed field k \mathbf {k} of characteristic 0 0 . We prove that if there is no rational function H ∈ k ( X ) H \in \mathbf {k}(X) such that H ∘ f = H H \circ f = H , then there exists a point x ∈ X ( k ) x \in X(\mathbf {k}) such that the forward orbit of x x under f f is Zariski dense in X X . This result gives us a positive answer to the Zariski dense orbit conjecture for endomorphisms of smooth projective surfaces. We also define a new topology on varieties over algebraically closed fields with fini
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Dissertations / Theses on the topic "Zariski topology"

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Guerville, Benoît. "Invariants Topologiques d'Arrangements de droites." Thesis, Pau, 2013. http://www.theses.fr/2013PAUU3033/document.

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Cette thèse est le point d’intersection entre deux facettes de l’étude des arrangements de droites : la combinatoire et la topologie. Dans une première partie nous avons étudié l’inclusion de la variété bord dans le complémentaire d’un arrangement. Nous avons ainsi généralisé le résultat d’E. Hironaka au cas de tous les arrangements complexes. Pour contourner les problèmes provenant des arrangements non réels, nous avons étudié le diagramme de câblage, dit wiring diagram, qui code la monodromie de tresses sous forme de tresse singulière. Pour pouvoir l'utiliser, nous avons implémenté un progra
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Marty, Florian. "Des ouverts Zariski et des morphismes lisses en géométrie relative." Toulouse 3, 2009. http://thesesups.ups-tlse.fr/540/.

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Dans cette thèse, l'auteur étudie la théorie des schémas relatifs telle qu'elle est définie par B. Toën et M. Vaquié dans leur article "Au dessous de Spec(Z)". Il se penche plus particulièrement sur l'étude des ouverts Zariski et des morphismes lisses dans un cadre relatif sans hypothèse d'additivité sur la catégorie de base. Le premier résultat obtenu est une description en terme d'idéaux premier relatifs de l'espace topologique de Zariski, associé à une schéma relatif affine. Le second résultat de la thèse est la définition d'une notion de morphisme lisse relatif, entre monoïdes, qui général
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de, Felipe Paramio Ana Belén. "Topologie des espaces de valuations et géométrie des singularités." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC136.

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On étudie la fibre de l'espace de Riemann-Zariski au-dessus d'un point fermé x d'une variété algébrique X définie sur un corps algébriquement clos. On caractérise son type d'homéomorphisme pour des points réguliers et des singularités normales de surface. Cela est fait en étudiant le lien avec l'entrelac non Archimédien normalisé de x dans X. On démontre qu'ils ont le même comportement<br>We study the fiber of the Riemann-Zariski space above a closed point x of an algebraic variety X defined over an algebraically closed field. We characterize its homeomorphism type for regular points and norma
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Nanni, Giacomo. "Varietà di Segre e di Veronese." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/20941/.

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L'obbiettivo della tesi è presentare due esempi classici di varietà proiettive: le varietà di Segre e di Veronese. Inizialmente si presentano alcuni risultati generali sugli insiemi algebrici affini e proiettivi, sugli anelli graduati e gli ideali omogenei, sulla corrispondenza tra insiemi algebrici proiettivi e ideali omogenei radicali e si costruisce la topologia di Zariski di Pn. Si costruiscono poi le varietà di Segre e le varietà di Veronese e si conclude con alcune considerazioni sulla cubica gobba.
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Floris, Enrica. "Deux aspects de la géométrie birationnelle des variétés algébriques : la formule du fibré canonique et la décomposition de Zariski." Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00861470.

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La formule du fibré canonique et la décomposition de Zariski sont deux outils très importants en géométrie birationnelle. La formule du fibré canonique pour une fibration f:(X,B)->Z consiste à écrire K_X+B comme tiré en arrière de K_Z+B_Z+M où B_Z contient des informations sur les fibres singulières et M s'appelle partie modulaire. Il a été conjecturé qu'il existe une modification birationnelle Z' de Z telle que M' est semiample, où M' est la partie modulaire induite par changement de base. Un diviseur pseudoeffectif admet une décomposition de Zariski s'il existent un diviseur nef P et un divi
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Ray, Samarpita. "Some results on Spectral spaces and Spectral sequences." Thesis, 2019. https://etd.iisc.ac.in/handle/2005/5128.

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This thesis is made up of two independent parts. We begin the first part by showing that the collection of all prime ideals of a monoid or, in other words, the spectrum of a commutative monoid, endowed with the Zariski topology is homeomorphic to the spectrum of a ring, i.e., it is a spectral space. Spectral spaces were introduced by M. Hochster and are widely studied in the literature. On the other hand, the theory of monoids became relevant in the context of what is known as “absolute algebraic geometry”. In this work, we present several naturally occurring classes of spectral spaces u
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Books on the topic "Zariski topology"

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Hrushovski, Ehud, and François Loeser. Continuity of homotopies. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0010.

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This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs i
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Hrushovski, Ehud, and François Loeser. The space of stably dominated types. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0003.

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This chapter introduces the space unit vector V of stably dominated types on a definable set V. It first endows unit vector V with a canonical structure of a (strict) pro-definable set before providing some examples of stably dominated types. It then endows unit vector V with the structure of a definable topological space, and the properties of this definable topology are discussed. It also examines the canonical embedding of V in unit vector V as the set of simple points. An essential feature in the approach used in this chapter is the existence of a canonical extension for a definable functi
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Book chapters on the topic "Zariski topology"

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Kemper, Gregor. "The Zariski Topology." In Graduate Texts in Mathematics. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03545-6_4.

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Scheiderer, Claus. "Relations to the Zariski topology." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0074287.

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Underwood, Robert G. "The Zariski Topology on the Spectrum." In An Introduction to Hopf Algebras. Springer New York, 2011. http://dx.doi.org/10.1007/978-0-387-72766-0_2.

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Parusiński, Adam. "Algebro-Geometric Equisingularity of Zariski." In Handbook of Geometry and Topology of Singularities II. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-78024-1_4.

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Ribón, Javier. "Description of the Zariski-Closure of a Group of Formal Diffeomorphisms." In Handbook of Geometry and Topology of Singularities VI: Foliations. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-54172-8_7.

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Brodmann, Markus. "Zariski-Topologie und Koordinatenringe." In Algebraische Geometrie. Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-9266-7_6.

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Laumon, Gérard, and Laurent Moret-Bailly. "Points d’un S-champ algébrique; topologie de Zariski." In Champs algébriques. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-540-24899-6_5.

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Yves, Diers. "Spectra." In Categories of Commutative Algebras. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535867.003.0004.

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Abstract The prime spectrum of an object A is the set of prime congruences on A with a topology called the Zariski topology. The open sets are defined by congruences on A, the closed sets by regular quotients of A, the affine open sets by codisjunctable congruences on A or singular quotients of A, and the affine subsets by simultaneously codisjunctable families of congruences on A or semisingular quotients of A. The maximal spectrum of A is the subspace of the prime spectrum whose elements are the maximal congruences on A. The patch spectrum of A is the patch space of the prime spectrum of A o
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"The K-Spectrum and the Zariski Topology." In IISc Lecture Notes Series. Co-Published with Indian Institute of Science (IISc), Bangalore, India, 2010. http://dx.doi.org/10.1142/9789814304573_0002.

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"Structure of varieties in the Zariski topology." In Graduate Studies in Mathematics. American Mathematical Society, 2022. http://dx.doi.org/10.1090/gsm/222/05.

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Conference papers on the topic "Zariski topology"

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Çeken, Seçil, Mustafa Alkan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Dual of Zariski Topology for Modules." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637758.

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Çeken, Seçil. "On a subspace of dual Zariski topology." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992456.

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Sanh, Nguyen Van, Le Phuong Thao, Noori F. A. Al-Mayahi, and Kar Ping Shum. "Zariski Topology of Prime Spectrum of a Module." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0037.

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