Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 2, pp. 551-555 (2002)
On the Intersection of Invariant Rings
Thomas Bayer
Institut für Informatik, Technische Universität München, 80290 München, Germany, e-mail: bayert@in.tum.de, www: http://www14.in.tum.de/personen/bayert
Abstract: Based on Weitzenböck's theorem and Nagata's counterexample for Hilbert's fourteenth problem we construct two finitely generated invariant rings $R,S \subset K[x_{1},x_{2},\ldots,x_{n}]$ s.t. the intersection $R \cap S$ is not finitely generated as a $ K$-algebra.
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