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.