Dutta, Amartya Kumar ; Gupta, Neena ; Onoda, Nobuharu (2020) On finite generation of Noetherian algebras over two-dimensional regular local rings Journal of Algebra, 560 . pp. 241-265. ISSN 0021-8693
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Official URL: http://doi.org/10.1016/j.jalgebra.2020.05.013
Related URL: http://dx.doi.org/10.1016/j.jalgebra.2020.05.013
Abstract
Let R be a complete regular local ring with an algebraically closed residue field and let A be a Noetherian R-subalgebra of the polynomial ring R[X]. It has been shown in \cite{DO2} that if dimR=1, then A is necessarily finitely generated over R. In this paper, we give necessary and sufficient conditions for A to be finitely generated over R when dimR=2 and present an example of a Noetherian normal non-finitely generated R-subalgebra of R[X] over R=C[[u,v]].
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Finite Generation; Subalgebra Of Polynomial Algebra; Dimension Formula; Nagata Ring; Complete Local Ring; Regular Local Ring; Krull Domain; Excellent Ring. |
| ID Code: | 121169 |
| Deposited On: | 12 Jul 2021 09:02 |
| Last Modified: | 12 Jul 2021 09:02 |
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