Article
| Title: | A note on linear derivations (English) |
| Author: | Patra, Amit |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 3 |
| Year: | 2024 |
| Pages: | 683-695 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | At first we prove some results on a general polynomial derivation using few results of linear derivation. Then we study the ring of constants of a linear derivation for some rings. We know that any linear derivation is a nonsimple derivation. In the last section we find the smallest integer $w > 1 $ such that the polynomial ring in $n$ variables is $w$-differentially simple, all $w$ derivations are nonsimple and the $w$ derivations set contains a linear derivation. (English) |
| Keyword: | linear derivation |
| Keyword: | ring of constant |
| Keyword: | Fermat ring |
| Keyword: | Darboux polynomial |
| Keyword: | simple derivation |
| MSC: | 13N15 |
| idZBL: | Zbl 07953672 |
| idMR: | MR4804954 |
| DOI: | 10.21136/CMJ.2024.0249-23 |
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| Date available: | 2024-10-03T12:33:17Z |
| Last updated: | 2024-12-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152575 |
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| Reference: | [4] Lequain, Y.: Differential simplicity and complete integral closure.Pac. J. Math. 36 (1971), 741-751. Zbl 0188.09702, MR 0284422, 10.2140/pjm.1971.36.741 |
| Reference: | [5] Nowicki, A.: Polynomial Derivations and Their Rings of Constants.Nicolaus Copernicus University Press, Toruń (1994). Zbl 1236.13023, MR 2553232 |
| Reference: | [6] Nowicki, A.: On the nonexistence of rational first integrals for systems of linear differential equations.Linear Algebra Appl. 235 (1996), 107-120. Zbl 0843.34013, MR 1374254, 10.1016/0024-3795(94)00122-7 |
| Reference: | [7] Nowicki, A., Zieliński, J.: Rational constants of monomial derivations.J. Algebra 302 (2006), 387-418. Zbl 1119.13021, MR 2236608, 10.1016/j.jalgebra.2006.02.034 |
| Reference: | [8] Veloso, M., Shestakov, I.: Rings of constants of linear derivations on Fermat rings.Commun. Algebra 46 (2018), 5469-5479. Zbl 1461.13031, MR 3923774, 10.1080/00927872.2018.1469032 |
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