Article
| Title: | Unimodular rows over Laurent polynomial rings (English) |
| Author: | Mnif, Abdessalem |
| Author: | Amidou, Morou |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 72 |
| Issue: | 4 |
| Year: | 2022 |
| Pages: | 927-934 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove that for any ring ${\bf R}$ of Krull dimension not greater than 1 and $n\geq 3$, the group ${\rm E}_{n}({\bf R}[X, X^{-1}])$ acts transitively on ${\rm Um}_{n}({\bf R} [X, X^{-1}])$. In particular, we obtain that for any ring ${\bf R}$ with Krull dimension not greater than 1, all finitely generated stably free modules over ${\bf R} [X, X^{-1}]$ are free. All the obtained results are proved constructively. (English) |
| Keyword: | Quillen-Suslin theorem |
| Keyword: | stably free module |
| Keyword: | Hermite ring conjecture |
| Keyword: | Laurent polynomial ring |
| Keyword: | constructive mathematics |
| MSC: | 03F65 |
| MSC: | 13C10 |
| MSC: | 14Q20 |
| MSC: | 19A13 |
| idZBL: | Zbl 07655772 |
| idMR: | MR4517585 |
| DOI: | 10.21136/CMJ.2022.0002-20 |
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| Date available: | 2022-11-28T11:31:31Z |
| Last updated: | 2023-04-11 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151118 |
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