Affineness on Noetherian graded rings, algebras and Hopf algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909538591965184 |
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| author | Jia, Huan Zhang, Yinhuo |
| author_facet | Jia, Huan Zhang, Yinhuo |
| contents | In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affineness on Noetherian graded rings, algebras and Hopf algebras Jia, Huan Zhang, Yinhuo Rings and Algebras In this note, we show that every Noetherian graded ring with an affine degree zero part is affine. As a result, a Noetherian graded Hopf algebra whose degree zero component is a commutative or a cocommutative Hopf subalgebra is affine. Moreover, we show that the braided Hopf algebra of a Noetherian graded Hopf algebra is affine. |
| title | Affineness on Noetherian graded rings, algebras and Hopf algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2503.12268 |