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

Authors

Amartya Kumar Dutta, Indian Statistical Institute, Kolkata
Neena Gupta, Indian Statistical Institute, Kolkata
Nobuharu Onoda, University of Fukui

Article Type

Research Article

Publication Title

Journal of Algebra

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 [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]].

First Page

241

Last Page

265

DOI

10.1016/j.jalgebra.2020.05.013

Publication Date

10-15-2020

Comments

Open Access, Green

Recommended Citation

Dutta, Amartya Kumar; Gupta, Neena; and Onoda, Nobuharu, "On finite generation of Noetherian algebras over two-dimensional regular local rings" (2020). Journal Articles. 105.
https://digitalcommons.isical.ac.in/journal-articles/105