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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{ADM_2013_16_1_a3,
     author = {P. Brumatti and M. Veloso},
     title = {On locally nilpotent derivations of {Fermat} rings},
     journal = {Algebra and discrete mathematics},
     pages = {20--32},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a3/}
}
TY  - JOUR
AU  - P. Brumatti
AU  - M. Veloso
TI  - On locally nilpotent derivations of Fermat rings
JO  - Algebra and discrete mathematics
PY  - 2013
SP  - 20
EP  - 32
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a3/
LA  - en
ID  - ADM_2013_16_1_a3
ER  - 
%0 Journal Article
%A P. Brumatti
%A M. Veloso
%T On locally nilpotent derivations of Fermat rings
%J Algebra and discrete mathematics
%D 2013
%P 20-32
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2013_16_1_a3/
%G en
%F ADM_2013_16_1_a3
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/

[1] D. Daigle, “Locally nilpotent derivations”, Lecture notes for the Setember School of algebraic geometry (Lukȩcin, Poland, Setember 2003) http://aix1.uottawa.ca/d̃daigle

[2] M. Ferreiro, Y. Lequain, A. Nowicki, “A note on locally nilpotent derivations”, J. Pure Appl. Algebra, 79 (1992), 45–50 | DOI | MR

[3] D. Fiston, S. Maubach, “Constructing (almost) rigid rings and a UFD having infinitely generated Derksen and Makar-Limanov invariant”, Canad. Math. Bull., 53:1 (2010), 77–86 | DOI | MR

[4] G. Freudenberg, Algebraic Theory of Locally Nilpotent Derivations, Encyclopaedia of Mathematical Sciences, 136, Springer-Verlag, Berlin–Heidelberg, 2006 | MR

[5] L. Makar-Limanov, “On the group of automorphisms of a surface $x^ny=P(z)$”, Israel J. Math., 121 (2001), 113–123 | DOI | MR | Zbl