Relevant bibliographies by topics / Hilbert’s Nullstellensatz

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Hilbert’s Nullstellensatz'

Author: Grafiati
Published: 4 June 2021
Last updated: 3 February 2022

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Journal articles on the topic "Hilbert’s Nullstellensatz"

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Reyes, Armando, and Jason Hernández-Mogollón. "A Survey on Some Algebraic Characterizations of Hilbert’s Nullstellensatz for Non-commutative Rings of Polynomial Type." Ingeniería y Ciencia 16, no. 31 (2020): 27–52. http://dx.doi.org/10.17230/ingciencia.16.31.2.

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In this paper we present a survey of some algebraic characterizations of Hilbert’s Nullstellensatz for non-commutative rings of polynomial type. Using several results established in the literature, we obtain a version of this theorem for the skew Poincaré-Birkhoff-Witt extensions. Once this is done, we illustrate the Nullstellensatz with examples appearing in noncommutative ring theory and non-commutative algebraic geometry.
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Pati, Vishwambhar. "Hilbert’s Nullstellensatz and the beginning of algebraic geometry." Resonance 4, no. 8 (1999): 36–57. http://dx.doi.org/10.1007/bf02837067.

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De Loera, Jesús A., Jon Lee, Peter N. Malkin, and Susan Margulies. "Computing infeasibility certificates for combinatorial problems through Hilbert’s Nullstellensatz." Journal of Symbolic Computation 46, no. 11 (2011): 1260–83. http://dx.doi.org/10.1016/j.jsc.2011.08.007.

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Shub, Michael, and Steve Smale. "On the intractability of Hilbert’s Nullstellensatz and an algebraic version of “ $NP\not=P$? ”." Duke Mathematical Journal 81, no. 1 (1995): 47–54. http://dx.doi.org/10.1215/s0012-7094-95-08105-8.

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MacCaull, W. A. "Hilbert's nullstellensatz revisited." Journal of Pure and Applied Algebra 54, no. 2-3 (1988): 289–97. http://dx.doi.org/10.1016/0022-4049(88)90035-7.

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LOERA, J. A., J. LEE, S. MARGULIES, and S. ONN. "Expressing Combinatorial Problems by Systems of Polynomial Equations and Hilbert's Nullstellensatz." Combinatorics, Probability and Computing 18, no. 4 (2009): 551–82. http://dx.doi.org/10.1017/s0963548309009894.

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Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colourable, Hamiltonian, etc.) if and only if a related system of polynomial equations has a solution.For an infeasible polynomial system, the (complex) Hilbert Nullstellensatz gives a certificate that the associated combinatorial problem is infeasible. Thus, unless P = NP, there must exist an infinite sequence of infeasible instances of each hard combinatorial problem for which the minimum degree of a Hilbert Nullste
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KAUCIKAS, ALGIRDAS, and ROBERT WISBAUER. "NONCOMMUTATIVE HILBERT RINGS." Journal of Algebra and Its Applications 03, no. 04 (2004): 437–43. http://dx.doi.org/10.1142/s0219498804000964.

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Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. This notion was extended to noncommutative rings in two different ways by the requirement that prime ideals are the intersection of maximal or of maximal left ideals, respectively. Here we propose to define noncommutative Hilbert rings by the property that strongly prime ideals are the intersection of maximal ideals. Unlike for the other definitions, these rings can be characterized by a contraction property: R is a Hilbert ring if and only if for all n∈ℕ every maximal ide
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Finocchiaro, Carmelo A., Marco Fontana, and Dario Spirito. "A topological version of Hilbert's Nullstellensatz." Journal of Algebra 461 (September 2016): 25–41. http://dx.doi.org/10.1016/j.jalgebra.2016.04.020.

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Perri, Tal, and Louis H. Rowen. "Kernels in tropical geometry and a Jordan–Hölder theorem." Journal of Algebra and Its Applications 17, no. 04 (2018): 1850066. http://dx.doi.org/10.1142/s0219498818500664.

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When considering affine tropical geometry, one often works over the max-plus algebra (or its supertropical analog), which, lacking negation, is a semifield (respectively, [Formula: see text]-semifield) rather than a field. One needs to utilize congruences rather than ideals, leading to a considerably more complicated theory. In his dissertation, the first author exploited the multiplicative structure of an idempotent semifield, which is a lattice ordered group, in place of the additive structure, in order to apply the extensive theory of chains of homomorphisms of groups. Reworking his dissert
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Koiran, Pascal. "Hilbert's Nullstellensatz Is in the Polynomial Hierarchy." Journal of Complexity 12, no. 4 (1996): 273–86. http://dx.doi.org/10.1006/jcom.1996.0019.

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Dissertations / Theses on the topic "Hilbert’s Nullstellensatz"

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Rigolli, Lorenzo. "Hilbert Nullstellensatz e alcune sue conseguenze geometriche." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2505/.

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Berthet, Jean. "Contributions à l’étude algébrique et géométrique des structures et théories du premier ordre." Thesis, Lyon 1, 2010. http://www.theses.fr/2010LYO10266/document.

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La notion de T-radical d’un idéal permet à G.Cherlin de démontrer un Nullstellensatz dans les théories inductives d’anneaux. Nous proposons une analyse modèle-théorique de phénomènes connexes. En premier lieu, une réciproque de ce théorème nous conduit à une caractérisation des corps algébriquement clos, suggérant une version “positive” du travail de Cherlin, la théorie des idéaux T-radiciels. Ceux-ci se caractérisent par un théorème de représentation et sont associés à un théorème des zéros “positif”. Ces résultats se généralisent à la logique du premier ordre : grâce à la notion de classe sp
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Amendola, Teresa. "Basi di Gröbner e anelli polinomiali." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19458/.

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In questo elaborato ci proponiamo di fornire alcuni strumenti utili per illustrare il collegamento tra varietà affini e ideali polinomiali. La tesi segue l'approccio computazionale e sfrutta quindi alcuni algoritmi per la dimostrazione dei risultati principali. Si prova il Teorema della Base di Hilbert e si introducono le basi di Gröbner per la dimostrazione del Nullstellensatz.
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Book chapters on the topic "Hilbert’s Nullstellensatz"

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Kemper, Gregor. "Hilbert’s Nullstellensatz." In Graduate Texts in Mathematics. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-03545-6_2.

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Lang, Serge. "Hilbert’s Nullstellensatz in Infinite-Dimensional Space." In Collected Papers. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-2118-0_2.

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Lang, Serge. "Hilbert’s Nullstellensatz in Infinite Dimensional Space." In Collected Papers I. Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4614-7383-1_2.

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Lipton, Richard J., and Kenneth W. Regan. "David Hilbert: The Nullstellensatz." In People, Problems, and Proofs. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-41422-0_45.

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Becker, Thomas, and Volker Weispfenning. "Field Extensions and the Hilbert Nullstellensatz." In Gröbner Bases. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0913-3_8.

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"Hilbert’s Nullstellensatz." In An Invitation to Model Theory. Cambridge University Press, 2019. http://dx.doi.org/10.1017/9781316683002.039.

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"V.17 Hilbert’s Nullstellensatz." In The Princeton Companion to Mathematics. Princeton University Press, 2010. http://dx.doi.org/10.1515/9781400830398.703a.

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Brownawell, W. Dale. "Aspects of the Hilbert Nullstellensatz." In New Advances in Transcendence Theory. Cambridge University Press, 1988. http://dx.doi.org/10.1017/cbo9780511897184.008.

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"21. The Hilbert basis theorem and the nullstellensatz." In Abstract Algebra. De Gruyter, 2019. http://dx.doi.org/10.1515/9783110603996-021.

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"21 The Hilbert Basis Theorem and the Nullstellensatz." In Abstract Algebra. DE GRUYTER, 2011. http://dx.doi.org/10.1515/9783110250091.312.

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Conference papers on the topic "Hilbert’s Nullstellensatz"

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Li, Zijia, and Andreas Mueller. "Mechanism Singularities Revisited From an Algebraic Viewpoint." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97742.

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Abstract It has become obvious that certain singular phenomena cannot be explained by a mere investigation of the configuration space, defined as the solution set of the loop closure equations. For example, it was observed that a particular 6R linkage, constructed by combination of two Goldberg 5R linkages, exhibits kinematic singularities at a smooth point in its configuration space. Such problems are addressed in this paper. To this end, an algebraic framework is used in which the constraints are formulated as polynomial equations using Study parameters. The algebraic object of study is the
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Kapur, Deepak. "Geometry theorem proving using Hilbert's Nullstellensatz." In the fifth ACM symposium. ACM Press, 1986. http://dx.doi.org/10.1145/32439.32479.

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De Loera, J. A., J. Lee, P. N. Malkin, and S. Margulies. "Hilbert's nullstellensatz and an algorithm for proving combinatorial infeasibility." In the twenty-first international symposium. ACM Press, 2008. http://dx.doi.org/10.1145/1390768.1390797.

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