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]].

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