Relevant bibliographies by topics / Locally nilpotent derivations

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  2. Dissertations / Theses
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Academic literature on the topic 'Locally nilpotent derivations'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Locally nilpotent derivations"

1

Karaś, Marek. "Locally Nilpotent Monomial Derivations." Bulletin of the Polish Academy of Sciences Mathematics 52, no. 2 (2004): 119–21. http://dx.doi.org/10.4064/ba52-2-2.

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LEVCHUK, VLADIMIR M., and OKSANA V. RADCHENKO. "DERIVATIONS OF THE LOCALLY NILPOTENT MATRIX RINGS." Journal of Algebra and Its Applications 09, no. 05 (2010): 717–24. http://dx.doi.org/10.1142/s0219498810004154.

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Derivations of the ring of all finitary niltriangular matrices over an arbitrary associative ring with identity for any chain of matrix indices are described. Every Lie or Jordan derivation is a derivation of this ring modulo third hypercenter.
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Finston, David R., and Sebastian Walcher. "Centralizers of locally nilpotent derivations." Journal of Pure and Applied Algebra 120, no. 1 (1997): 39–49. http://dx.doi.org/10.1016/s0022-4049(96)00064-3.

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El Kahoui, M’hammed. "Subresultants and locally nilpotent derivations." Linear Algebra and its Applications 380 (March 2004): 253–61. http://dx.doi.org/10.1016/j.laa.2003.11.004.

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Tanaka, Mikiya. "Locally nilpotent derivations on modules." Journal of Mathematics of Kyoto University 49, no. 1 (2009): 131–59. http://dx.doi.org/10.1215/kjm/1248983033.

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Matveev, D. A. "Commuting homogeneous locally nilpotent derivations." Sbornik: Mathematics 210, no. 11 (2019): 1609–32. http://dx.doi.org/10.1070/sm9132.

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BERGEN, JEFFREY, and PIOTR GRZESZCZUK. "GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS." Glasgow Mathematical Journal 57, no. 3 (2014): 555–67. http://dx.doi.org/10.1017/s0017089514000482.

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AbstractLet A be a domain over an algebraically closed field with Gelfand–Kirillov dimension in the interval [2,3). We prove that if A has two locally nilpotent skew derivations satisfying some natural conditions, then A must be one of five algebras. All five algebras are Noetherian, finitely generated, and have Gelfand–Kirillov dimension equal to 2. We also obtain some results comparing the Gelfand–Kirillov dimension of an algebra to its subring of invariants under a locally nilpotent skew derivation.
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Zhao, Wenhua. "Some open problems on locally finite or locally nilpotent derivations and ℰ-derivations". Communications in Contemporary Mathematics 20, № 04 (2018): 1750056. http://dx.doi.org/10.1142/s0219199717500560.

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Let [Formula: see text] be a commutative ring and [Formula: see text] an [Formula: see text]-algebra. An [Formula: see text]-[Formula: see text]-derivation of [Formula: see text] is an [Formula: see text]-linear map of the form [Formula: see text] for some [Formula: see text]-algebra endomorphism [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the identity map of [Formula: see text]. In this paper, we discuss some open problems on whether or not the image of a locally finite (LF) [Formula: see text]-derivation or [Formula: see text]-[Formula: see text]-derivation
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Kuroda, Shigeru. "Van den Essen's conjecture on the kernel of a derivation having a slice." Journal of Algebra and Its Applications 14, no. 09 (2015): 1540003. http://dx.doi.org/10.1142/s0219498815400034.

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The problem of finite generation of the kernel of a derivation of a polynomial ring is a special case of Hilbert's Fourteenth Problem. It is well known that the answer is affirmative if the derivation is locally nilpotent and having a slice. Van den Essen (1995) conjectured that there exists a counterexample for non-locally nilpotent derivations with a slice. In this paper, we solve this conjecture in the affirmative.
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El Kahoui, M’hammed, and Mustapha Ouali. "Locally nilpotent derivations of factorial domains." Journal of Algebra and Its Applications 18, no. 12 (2019): 1950222. http://dx.doi.org/10.1142/s0219498819502220.

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Let [Formula: see text] be factorial domains containing [Formula: see text]. In this paper, we give a criterion, in terms of locally nilpotent derivations, for [Formula: see text] to be [Formula: see text]-isomorphic to [Formula: see text], where [Formula: see text] is nonzero and [Formula: see text]. As a consequence, we retrieve a recent result due to Masuda [Families of hypersurfaces with noncancellation property, Proc. Amer. Math. Soc. 145(4) (2017) 1439–1452] characterizing Danielewski hypersurfaces whose coordinate ring is factorial. We also apply our criterion to the study of triangular
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Dissertations / Theses on the topic "Locally nilpotent derivations"

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Wang, Zhiqing. "Locally nilpotent derivations of polynomial rings." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0018/NQ48119.pdf.

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Chitayat, Michael. "Locally Nilpotent Derivations and Their Quasi-Extensions." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/35072.

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In this thesis, we introduce the theory of locally nilpotent derivations and use it to compute certain ring invariants. We prove some results about quasi-extensions of derivations and use them to show that certain rings are non-rigid. Our main result states that if k is a field of characteristic zero, C is an affine k-domain and B = C[T,Y] / < T^nY - f(T) >, where n >= 2 and f(T) \in C[T] is such that delta^2(f(0)) != 0 for all nonzero locally nilpotent derivations delta of C, then ML(B) != k. This shows in particular that the ring B is not a polynomial ring over k.
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Khoury, Joseph. "Locally nilpotent derivations and their rings of constants." Thesis, University of Ottawa (Canada), 2001. http://hdl.handle.net/10393/9028.

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Given a UFD R containing Q , we study R-elementary derivations of B = R[Y1,..., Ym], i.e., R-derivations satisfying D( Yi) &isin; R for all i; in the particular case of m = 3, we will show that if R is a polynomial ring in n variables over a field k (of characteristic zero), and a1, a3, a3 &isin; R are three monomials, then the kernel of the derivation i=13ai6 /6Yi of B is generated over R by at most three linear elements in the Yi's. This gives a partial answer to a question of A. van den Essen ([27]) about the existence of elementary derivations in dimension six whose kernels are not
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EL, Houari Hassan. "Algorithms for locally nilpotent derivations in dimension two and three." Limoges, 2007. https://aurore.unilim.fr/theses/nxfile/default/7d0e7c9d-8bec-4ccf-af81-92abce4349cb/blobholder:0/2007LIMO4049.pdf.

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Les dérivations localement nilpotentes sur les anneaux des polynômes sont des objets de grande importance dans beaucoup de domaines de mathématiques. Durant la dernière décennie, elles ont connu un véritable progrès et sont devenues un élément essentiel pour la compréhension de la géométrie algébrique affine et d’algèbre commutative. Cette importance est due au fait que certains problèmes classiques dans ces domaines, telles que la conjecture jacobienne, le problème d’élimination, le problème de plongement et le problème de linéarisation, ont été reformulés dans la théorie des dérivations loca
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Nur, Alexandra. "Locally Nilpotent Derivations and the Cancellation Problem in Affine Algebraic Geometry." Thesis, University of Ottawa (Canada), 2011. http://hdl.handle.net/10393/28926.

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Let K be a field of characteristic zero and let R [n] denote the polynomial ring in n variables over a ring R for any n &isin; N , n > 0. We present some basic theory for the study of locally nilpotent derivations as an effective tool in algebraic geometry. Using this tool, we examine the Cancellation Problem in affine algebraic geometry, which asks: Let A be a K -algebra such that A[1] = K [n+1]. Does it follow that A = K [n]? This problem is open for n > 2. We present the solutions to the cases n = 1 and n = 2, in the latter case essentially following the algebraic method of Cr
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Nyobe, Likeng Samuel Aristide. "Locally Nilpotent Derivations on Polynomial Rings in Two Variables over a Field of Characteristic Zero." Thesis, Université d'Ottawa / University of Ottawa, 2017. http://hdl.handle.net/10393/35906.

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The main goal of this thesis is to present the theory of Locally Nilpotent Derivations and to show how it can be used to investigate the structure of the polynomial ring in two variables k[X;Y] over a field k of characteristic zero. The thesis gives a com- plete proof of Rentschler's Theorem, which describes all locally nilpotent derivations of k[X;Y]. Then we present Rentschler's proof of Jung's Theorem, which partially describes the group of automorphisms of k[X;Y]. Finally, we present the proof of the Structure Theorem for the group of automorphisms of k[X;Y].
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Merighe, Liliam Carsava. "Uma introdução às derivações localmente nilpotentes com uma aplicação ao 14º problema de Hilbert." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-05082015-102547/.

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O principal objetivo desta dissertação é estudar um contraexemplo para o Décimo Quarto Problema de Hilbert no caso de dimensão n = 5, que foi apresentado por Arno van den Essen ([6]) em 2006 e que é baseado em um contraexemplo de D. Daigle e G. Freudenburg ([4]). Para isso, serão estudados os conceitos fundamentais da teoria de derivações e os princípios básicos das derivações localmente nilpotentes, bem como seus respectivos corolários. Dentre esses princípios encontra-se o Princípio 13, que garante que, se B é uma k- álgebra polinomial, digamos B = k[x1; ..., xn], (onde k é um corpo de cara
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Abreu, Kelyane Barboza de. "Derivações localmente nilpotentes e os teoremas de Rentschler e Jung." Universidade Federal da Paraí­ba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7438.

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Made available in DSpace on 2015-05-15T11:46:20Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 685495 bytes, checksum: 924951307927847259c1bd0253812600 (MD5) Previous issue date: 2014-02-19<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The main goal of this work is to furnish a proof of the well-known Rentschler s Theorem, which describes the structure of the locally nilpotent derivations on the polynomial ring in two indeterminates (over a field of characteristic zero), up to conjugation by tame automorphisms. As a central application of this result, we prov
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Hedén, Isac. "Ga-actions on Complex Affine Threefolds." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-203708.

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This  thesis  consists  of two papers  and  a summary.  The  papers  both  deal with  affine algebraic complex  varieties,  and  in particular such  varieties  in dimension  three  that have a non-trivial action  of one of the  one-dimensional  algebraic  groups  Ga   :=  (C, +) and  Gm  :=  (C*, ·).  The methods  used  involve  blowing up  of subvarieties, the correspondances between  Ga - and  Gm - actions  on an affine variety  X with locally nilpotent derivations  and Z-gradings  respectively  on O(X) and passing from a filtered algebra  A to its associated graded  algebra  gr(A). In Paper
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Books on the topic "Locally nilpotent derivations"

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2010.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2017.

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Freudenburg, Gene. Algebraic Theory of Locally Nilpotent Derivations. Springer, 2018.

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Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/978-3-540-29523-5.

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Algebraic Theory of Locally Nilpotent Derivations (Encyclopaedia of Mathematical Sciences). Springer, 2006.

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Book chapters on the topic "Locally nilpotent derivations"

1

Daigle, Daniel. "Locally Nilpotent Sets of Derivations." In Polynomial Rings and Affine Algebraic Geometry. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42136-6_2.

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Makar-Limanov, L. "Locally nilpotent derivations of affine domains." In CRM Proceedings and Lecture Notes. American Mathematical Society, 2011. http://dx.doi.org/10.1090/crmp/054/12.

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Freudenburg, Gene. "First Principles." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_1.

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Freudenburg, Gene. "Slices, Embeddings and Cancellation." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_10.

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Freudenburg, Gene. "Epilogue." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_11.

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Freudenburg, Gene. "Further Properties of LNDs." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_2.

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Freudenburg, Gene. "Polynomial Rings." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_3.

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Freudenburg, Gene. "Dimension Two." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_4.

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Freudenburg, Gene. "Dimension Three." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_5.

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Freudenburg, Gene. "Linear Actions of Unipotent Groups." In Algebraic Theory of Locally Nilpotent Derivations. Springer Berlin Heidelberg, 2017. http://dx.doi.org/10.1007/978-3-662-55350-3_6.

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Journal articles
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