Geodesic
Images of locally nilpotent derivations of bivariate polynomial algebras over a domain
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 599-610 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let $R$ be a domain containing a field of characteristic zero. We prove that, when $R$ is a one-dimensional unique factorization domain, the image of any locally nilpotent $R$-derivation of the bivariate polynomial algebra $R[x,y]$ is a Mathieu-Zhao subspace. Moreover, we prove that, when $R$ is a Dedekind domain, the image of a locally nilpotent $R$-derivation of $R[x,y]$ with some additional conditions is a Mathieu-Zhao subspace.
We study the LND conjecture concerning the images of locally nilpotent derivations, which arose from the Jacobian conjecture. Let $R$ be a domain containing a field of characteristic zero. We prove that, when $R$ is a one-dimensional unique factorization domain, the image of any locally nilpotent $R$-derivation of the bivariate polynomial algebra $R[x,y]$ is a Mathieu-Zhao subspace. Moreover, we prove that, when $R$ is a Dedekind domain, the image of a locally nilpotent $R$-derivation of $R[x,y]$ with some additional conditions is a Mathieu-Zhao subspace.
DOI : 10.21136/CMJ.2024.0008-24
Classification : 13N15, 14R10
Keywords: locally nilpotent derivation; Jacobian conjecture; LND conjecture; Mathieu-Zhao subspace 
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     title = {Images of locally nilpotent derivations of bivariate polynomial algebras over a domain},
     journal = {Czechoslovak Mathematical Journal},
     pages = {599--610},
     year = {2024},
     volume = {74},
     number = {2},
     doi = {10.21136/CMJ.2024.0008-24},
     mrnumber = {4764542},
     zbl = {07893401},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0008-24/}
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Sun, Xiaosong; Wang, Beini. Images of locally nilpotent derivations of bivariate polynomial algebras over a domain. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 599-610. doi: 10.21136/CMJ.2024.0008-24

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