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RESEARCH ARTICLE

On locally nilpotent derivations of Fermat rings

P. Brumatti^a, M. Veloso<sup>b

a</sup> IMECC-Unicamp, Rua Sérgio Buarque de Holanda 651, Cx. P. 6065, 13083-859, Campinas-SP, Brazil
^b Defim-UFSJ, Rodovia MG 443 Km 7, 36420-000, Ouro Branco-MG, Brazil

Abstract: 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 $\mathbb{C}$.

Keywords: Locally Nilpotente Derivations, ML-invariant, Fermat ring.

MSC: 14R10, 13N15, 13A50

Received: 06.09.2010
Revised: 05.04.2013

Language: English

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