On invertibility of some polynomial maps
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910080889257984 |
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| author | Bekbaev, U. |
| author_facet | Bekbaev, U. |
| contents | Over an algebraically closed field $\mathbb{F}$ of zero characteristic polynomial map $ξ: \mathbb{F}^n\rightarrow \mathbb{F}^n$ of the form $ξ(x)=x-((xA_1)^{3}, (xA_2)^{3},..., (xA_n)^{3})$, where $x=(x_1,x_2,...,x_n)$ a row vector of variables, $A_i\in \mathbb{F}^n$ are column vectors, is considered. It is shown that if $\det(\partialξ(x))=1$, then $ξ$ is injective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04363 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On invertibility of some polynomial maps Bekbaev, U. Rings and Algebras 14R15, 13F20 Over an algebraically closed field $\mathbb{F}$ of zero characteristic polynomial map $ξ: \mathbb{F}^n\rightarrow \mathbb{F}^n$ of the form $ξ(x)=x-((xA_1)^{3}, (xA_2)^{3},..., (xA_n)^{3})$, where $x=(x_1,x_2,...,x_n)$ a row vector of variables, $A_i\in \mathbb{F}^n$ are column vectors, is considered. It is shown that if $\det(\partialξ(x))=1$, then $ξ$ is injective. |
| title | On invertibility of some polynomial maps |
| topic | Rings and Algebras 14R15, 13F20 |
| url | https://arxiv.org/abs/2512.04363 |