### On locally nilpotent derivations of Fermat rings

#### 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

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