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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2510.03775 |
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| _version_ | 1866915939886301184 |
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| author | Van Hoang, Dinh Toan, Phan Thanh |
| author_facet | Van Hoang, Dinh Toan, Phan Thanh |
| contents | The classical Noether Normalization Lemma states that if $S$ is a finitely generated algebra over a field $k$, then there exist elements $x_1,\dots,x_n$ which are algebraically independent over $k$ such that $S$ is a finite module over $k[x_1,\dots,x_n]$. This lemma has been studied intensively in different flavors. In 2024, Elad Paran and Thieu N. Vo successfully generalized this lemma for the case when $S$ is a quotient ring of the skew polynomial ring $D[x_1,\dots,x_n;σ_1,\dots,σ_n]$. In this paper, we investigate this lemma in a more general setting when $S$ is a quotient ring of an iterated skew polynomial ring $D[x_1;σ_1,δ_1]\dots[x_n;σ_n,δ_n]$. We extend several key results of Elad Paran and Thieu N. Vo to this broader context and introduce a new version of Combinatorial Nullstellensatz over division rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03775 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Noether's normalization in iterated skew polynomial rings Van Hoang, Dinh Toan, Phan Thanh Rings and Algebras The classical Noether Normalization Lemma states that if $S$ is a finitely generated algebra over a field $k$, then there exist elements $x_1,\dots,x_n$ which are algebraically independent over $k$ such that $S$ is a finite module over $k[x_1,\dots,x_n]$. This lemma has been studied intensively in different flavors. In 2024, Elad Paran and Thieu N. Vo successfully generalized this lemma for the case when $S$ is a quotient ring of the skew polynomial ring $D[x_1,\dots,x_n;σ_1,\dots,σ_n]$. In this paper, we investigate this lemma in a more general setting when $S$ is a quotient ring of an iterated skew polynomial ring $D[x_1;σ_1,δ_1]\dots[x_n;σ_n,δ_n]$. We extend several key results of Elad Paran and Thieu N. Vo to this broader context and introduce a new version of Combinatorial Nullstellensatz over division rings. |
| title | Noether's normalization in iterated skew polynomial rings |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.03775 |