Subrings of polynomial rings and the conjectures of Eisenbud and Evans
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911093970960384 |
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| author | Banerjee, Sourjya |
| author_facet | Banerjee, Sourjya |
| contents | Let $R$ be a commutative Noetherian ring of dimension $d$. In 1973, Eisenbud and Evans proposed three conjectures on the polynomial ring $R[T]$. These conjectures were settled in the affirmative by Sathaye, Mohan Kumar and Plumstead. One of the primary objectives of this article is to investigate the validity of these conjectures over Noetherian subrings of $R[T]$ of dimension $d+1$, containing $R$. We formulate a class of such rings, which includes polynomial rings, Rees algebras, Rees-like algebras and Noetherian symbolic Rees algebras, and exhibit that all three conjectures hold for rings belonging to this class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05001 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Subrings of polynomial rings and the conjectures of Eisenbud and Evans Banerjee, Sourjya Commutative Algebra 19A15, 13C10, 19A13 Let $R$ be a commutative Noetherian ring of dimension $d$. In 1973, Eisenbud and Evans proposed three conjectures on the polynomial ring $R[T]$. These conjectures were settled in the affirmative by Sathaye, Mohan Kumar and Plumstead. One of the primary objectives of this article is to investigate the validity of these conjectures over Noetherian subrings of $R[T]$ of dimension $d+1$, containing $R$. We formulate a class of such rings, which includes polynomial rings, Rees algebras, Rees-like algebras and Noetherian symbolic Rees algebras, and exhibit that all three conjectures hold for rings belonging to this class. |
| title | Subrings of polynomial rings and the conjectures of Eisenbud and Evans |
| topic | Commutative Algebra 19A15, 13C10, 19A13 |
| url | https://arxiv.org/abs/2301.05001 |