On finite generation of Noetherian algebras over two-dimensional regular local rings
Journal of Algebra
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  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]].
Dutta, Amartya Kumar; Gupta, Neena; and Onoda, Nobuharu, "On finite generation of Noetherian algebras over two-dimensional regular local rings" (2020). Journal Articles. 105.