Výsledky vyhledávání - "Arno van den Essen"

Autor: Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 113-177
Frontiers in Mathematics ISBN: 9783030605339

Throughout this section k denotes an algebraically closed field of characteristic zero. But, as the reader can check, most of the calculations done after Corollary 5.1.3 work equally well if k is just a commutative \(\mathbb Q\)-algebra.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bb84c2cafe49c42c8e4360dcfa9d5540
https://repository.ubn.ru.nl/handle/2066/234048

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The Shestakov–Umirbaev Theory and Nagata’s Conjecture

Autor: Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 1-42
Frontiers in Mathematics ISBN: 9783030605339

As discussed in the introduction of the book by van den Essen (Polynomial Automorphisms and the Jacobian Conjecture, Prog. Math., vol. 190, Birkhauser Verlag, Basel, 2000), Nagata conjectured that there exist wild polynomial automorphisms in three va

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8d95be874e381f07e094982dc6a9726
https://repository.ubn.ru.nl/handle/2066/234073

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The Jacobian Conjecture: New Equivalences

Autor: Arno van den Essen, Anthony J. Crachiola, Shigeru Kuroda

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 91-111
Frontiers in Mathematics ISBN: 9783030605339

As we have seen in van den Essen (Polynomial Automorphisms and the Jacobian Conjecture, Prog. Math., vol. 190, Birkhauser Verlag, Basel, 2000), there are various equivalent formulations of the Jacobian Conjecture. The aim of this chapter is to give f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f847404ea896d4dc05a47606e9d7e737
https://repository.ubn.ru.nl/handle/2066/234071

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Counterexamples to Hilbert’s Fourteenth Problem

Autor: Arno van den Essen, Shigeru Kuroda, Anthony J. Crachiola

Publikováno v: Essen, A. van den (ed.), Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century, pp. 43-64
Frontiers in Mathematics ISBN: 9783030605339

Item does not contain fulltext Let k be a field, x = k[x1, …, xn] the polynomial ring in n variables over k, k(x) the field of fractions of k[x], and L a subfield of k(x) containing k. Hilbert’s fourteenth problem asks whether the k-algebra L ∩

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https://repository.ubn.ru.nl/handle/2066/234021

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A new class of Nilpotent Jacobians in any dimension

Autor: Álvaro Castañeda, Arno van den Essen

Publikováno v: Journal of Algebra, 566, 283-301
Journal of Algebra, 566, pp. 283-301

The classification of the nilpotent Jacobians with some structure has been an object of study because of its relationship with the Jacobian conjecture. In this paper we classify the polynomial maps in dimension n of the form H = ( u ( x , y ) , u 2 (

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http://hdl.handle.net/2066/226085

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Mathieu-Zhao Spaces and the Jacobian Conjecture

Autor: Arno van den Essen

Publikováno v: Springer Proceedings in Mathematics & Statistics ISBN: 9783030421359

In this paper we define the notion of a Mathieu-Zhao space, give various examples of this concept and use the framework of these Mathieu-Zhao spaces to describe a chain of challenging conjectures, all implying the Jacobian Conjecture.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7ea27ebcc215dfd8a4a33a3ab52044f9
https://doi.org/10.1007/978-3-030-42136-6_14

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Mathieu–Zhao spaces of univariate polynomial rings with non-zero strong radical

Autor: Simeon Nieman, Arno van den Essen

Publikováno v: Journal of Pure and Applied Algebra, 220, 3300-3306
Journal of Pure and Applied Algebra, 220, 9, pp. 3300-3306

We describe all Mathieu–Zhao spaces of the univariate polynomial ring k[t]k[t] (k an algebraically closed field of characteristic zero) which have a non-zero strong radical.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5db9ef410f8e0264ef29fae4c204d5f7
https://doi.org/10.1016/j.jpaa.2016.02.015

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On images of locally finite derivations and E-derivations

Autor: Wenhua Zhao, Arno van den Essen

Publikováno v: Journal of Pure and Applied Algebra, 223, 4, pp. 1689-1698
Journal of Pure and Applied Algebra, 223, 1689-1698

Some cases of the LFED Conjecture, proposed by the second author [15] , for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions k ( x ) of the polynomial algebra k [ x ] , the f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94ef8500958e0f03bb5868199e6cee75
https://doi.org/10.1016/j.jpaa.2018.07.002

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Monomial preserving derivations and Mathieu–Zhao subspaces

Autor: Arno van den Essen, Xiaosong Sun

Publikováno v: Journal of Pure and Applied Algebra, 222, 3219-3223
Journal of Pure and Applied Algebra, 222, 10, pp. 3219-3223

In this paper, we give a complete description of when the image of a monomial preserving derivation (or E -derivation) of the polynomial algebra over a field of characteristic zero is a Mathieu–Zhao subspace. In particular we show that the LFED and

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6b4ef50b1ff054340189a92b2066bc9e
http://hdl.handle.net/2066/191524

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