Let k be a field and G be a finite subgroup of \( \GL_n(\mathbb Z) \). We show that the ring of multiplicative invariants has a finite SAGBI basis if and only if G is generated by reflections.
Cite this article
Zinovy Reichstein, SAGBI bases in rings of multiplicative invariants. Comment. Math. Helv. 78 (2003), no. 1, pp. 185–202DOI 10.1007/S000140300008