Manfred Göbel
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The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBI Bases with Respect to Any Admissible Orderdmtcs:259 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 1999,
Vol. 3 no. 2
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https://doi.org/10.46298/dmtcs.259
The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBI Bases with Respect to Any Admissible OrderArticle
Authors: Manfred Göbel 1
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Manfred Göbel
1 German Remote Sensing Data Center
We prove the existence of an invariant ring \textbfC[X_1,...,X_n]^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.
Mohammed Tesemma, 2008, On initial algebras of multiplicative invariants, Journal of Algebra, 320, 11, pp. 3851-3865, 10.1016/j.jalgebra.2008.06.030.