Geodesic
On locally nilpotent derivations of Fermat rings
Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 20-32

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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, Fermat ring.
Mots-clés : ML-invariant 
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P. Brumatti; M. Veloso. On locally nilpotent derivations of Fermat rings. Algebra and discrete mathematics, Tome 16 (2013) no. 1, pp. 20-32. http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a3/