Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4589166 | Journal of Algebra | 2007 | 10 Pages |
Abstract
Let k[X] be the polynomial ring in n variables over a field k for some n∈N, and k(X) its field of fractions. Assume that L is a subfield of k(X) containing k over which k(X) is algebraic. In spite of being an important issue in Hilbert's Fourteenth Problem, relations between finite generation of the k-subalgebra L∩k[X] of k[X] and the extension degree [k(X):L] of k(X) over L have not been investigated. In the present paper, we give an example of L with [k(X):L]=d such that L∩k[X] is not finitely generated for each d∈N with d⩾3 for n=3.
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