Tohoku Mathematical Journal
2004
December
SECOND SERIES VOL. 56, NO. 4

Tohoku Math. J.
56 (2004), 501-522

Title A GENERALIZATION OF ROBERTS' COUNTEREXAMPLE TO THE FOURTEENTH PROBLEM OF HILBERT

Author Shigeru Kuroda

(Received February 28, 2003, revised July 17, 2003)
Abstract. We generalize Roberts' counterexample to the fourteenth problem of Hilbert, and give a sufficient condition for certain invariant rings not to be finitely generated. It shows that there exist a lot of counterexamples of this type. We also determine the initial algebra of Roberts' counterexample for some monomial order.

2000 Mathematics Subject Classification. Primary 13A50; Secondary 13E15, 13N15, 13P10, 14R20.

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