Article
| Title: | Images of locally nilpotent derivations of bivariate polynomial algebras over a domain (English) |
| Author: | Sun, Xiaosong |
| Author: | Wang, Beini |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 2 |
| Year: | 2024 |
| Pages: | 599-610 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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. (English) |
| Keyword: | locally nilpotent derivation |
| Keyword: | Jacobian conjecture |
| Keyword: | LND conjecture |
| Keyword: | Mathieu-Zhao subspace |
| MSC: | 13N15 |
| MSC: | 14R10 |
| DOI: | 10.21136/CMJ.2024.0008-24 |
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| Date available: | 2024-07-10T14:58:03Z |
| Last updated: | 2024-07-15 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152460 |
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