On locally nilpotent derivations of Fermat rings
Let \(B_n^m =\frac{\mathbb{C}[X_1,\ldots, X_n]}{(X_1^m+\cdots +X_n^m)}\) (Fermat ring), where \(m\geq2\) and \(n\geq3\). In a recent paper D. Fiston and S. Maubach show that for \(m\geq n^2-2n\) the unique locally nilpotent derivation of \(B_n^m\) is the zero derivation. In this note we prove th...
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/752 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-7522018-04-26T01:26:05Z On locally nilpotent derivations of Fermat rings Brumatti, Paulo Roberto Veloso, Marcelo Oliveira Locally Nilpotente Derivations, ML-invariant, Fermat ring 14R10, 13N15, 13A50 Let \(B_n^m =\frac{\mathbb{C}[X_1,\ldots, X_n]}{(X_1^m+\cdots +X_n^m)}\) (Fermat ring), where \(m\geq2\) and \(n\geq3\). In a recent paper D. Fiston and S. Maubach show that for \(m\geq n^2-2n\) the unique locally nilpotent derivation of \(B_n^m\) is the zero derivation. In this note we prove that the ring \(B_n^2\) has non-zero irreducible locally nilpotent derivations, which are explicitly presented, and that its ML-invariant is \(\mathbb{C}\). Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/752 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/752/281 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Locally Nilpotente Derivations ML-invariant Fermat ring 14R10 13N15 13A50 |
| spellingShingle |
Locally Nilpotente Derivations ML-invariant Fermat ring 14R10 13N15 13A50 Brumatti, Paulo Roberto Veloso, Marcelo Oliveira On locally nilpotent derivations of Fermat rings |
| topic_facet |
Locally Nilpotente Derivations ML-invariant Fermat ring 14R10 13N15 13A50 |
| format |
Article |
| author |
Brumatti, Paulo Roberto Veloso, Marcelo Oliveira |
| author_facet |
Brumatti, Paulo Roberto Veloso, Marcelo Oliveira |
| author_sort |
Brumatti, Paulo Roberto |
| title |
On locally nilpotent derivations of Fermat rings |
| title_short |
On locally nilpotent derivations of Fermat rings |
| title_full |
On locally nilpotent derivations of Fermat rings |
| title_fullStr |
On locally nilpotent derivations of Fermat rings |
| title_full_unstemmed |
On locally nilpotent derivations of Fermat rings |
| title_sort |
on locally nilpotent derivations of fermat rings |
| description |
Let \(B_n^m =\frac{\mathbb{C}[X_1,\ldots, X_n]}{(X_1^m+\cdots +X_n^m)}\) (Fermat ring), where \(m\geq2\) and \(n\geq3\). In a recent paper D. Fiston and S. Maubach show that for \(m\geq n^2-2n\) the unique locally nilpotent derivation of \(B_n^m\) is the zero derivation. In this note we prove that the ring \(B_n^2\) has non-zero irreducible locally nilpotent derivations, which are explicitly presented, and that its ML-invariant is \(\mathbb{C}\). |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/752 |
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AT brumattipauloroberto onlocallynilpotentderivationsoffermatrings AT velosomarcelooliveira onlocallynilpotentderivationsoffermatrings |
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2024-04-12T06:26:36Z |
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2024-04-12T06:26:36Z |
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1796109222483591168 |