Discrete Mathematics & Theoretical Computer Science, Vol 3, No 2 (1999)

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The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBI Bases with Respect to Any Admissible Order

Manfred Göbel


We prove the existence of an invariant ring C[X1,...,Xn]T generated by elements with a total degree of at most 2, which has no finite SAGBI basis with respect to any admissible order. Therefore, 2 is the optimal lower bound for the total degree of generators of invariant rings with such a property.

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