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Images of locally nilpotent derivations of polynomial algebras in three variables. (English) Zbl 1451.14172

In the paper, the authors study the images of the locally nilpotent derivations in dimension three. They first prove that the image of a rank two locally nilpotent derivation in dimension three is a Mathieu-Zhao subspace of \(K[x,y,z]\) in Section 3. In particular, they prove that the image of a triangular derivation or a linear locally nilpotent derivation in dimension three is a Mathieu-Zhao subspace of \(K[x,y,z]\). Then they prove that the image of a homogeneous locally nilpotent derivation is a Mathieu-Zhao subspace of \(K[x,y,z]\) in the last two sections.
Reviewer: Yan Dan (Changsha)

MSC:

14R10 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
14R15 Jacobian problem
13N15 Derivations and commutative rings
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