Hilbert's Fourteenth Problem and algebraic extensions

Abstract: Let be the polynomial ring in n variables over a field k for some , and its field of fractions. Assume that L is a subfield of containing k over which is algebraic. In spite of being an important issue in Hilbert''s Fourteenth Problem, relations between finite generation of the k-subalgebra of and the extension degree of over L have not been investigated. In the present paper, we give an example of L with such that is not finitely generated for each with for . [Copyright &y& Elsevier]