On finite generation of Noetherian algebras over two-dimensional regular local rings

JOURNAL OF ALGEBRA

卷:560

Article

Dutta, Amartya Kumar¹  Gupta, Neena¹  Onoda, Nobuharu^2,3 

[1] Indian Stat Inst, Stat Math Unit, 203 BT Rd, Kolkata 700108, India

[2] Univ Fukui, Dept Math, Bunkyo 3-9-1, Fukui 9108507, Japan

[3] Open Univ Japan, Fukui Study Ctr, AOSSA 7F, Teyose 1-4-1, Fukui 9100858, Japan

关键词: Finite generation;    Subalgebra of polynomial algebra;    Dimension formula;    Nagata ring;    Complete local ring;    Regular local ring;    Krull domain;    Excellent ring;   

DOI  :  10.1016/j.jalgebra.2020.05.013

来源: Elsevier

【 摘 要 】

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 [4] that if dim R = 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 dim R = 2 and present an example of a Noetherian normal non-finitely generated R-subalgebra of R[X] over R = C[[u , v]]. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free