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

*Manfred Göbel*

#### Abstract

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.Full Text: GZIP Compressed PostScript PostScript PDF original HTML abstract page