#### Z. Reichstein, * SAGBI bases in rings
of multiplicative invariants, *
Commentarii Math Helvetici 78 (2003), 185 -- 202.

**Abstract:** The subject matter of this paper
falls somewhere between computational algebra, invariant theory,
and the combinatorics of polyhedral cones in R^n. The main result
is as follows.
Let k be a field and G be a finite subgroup of GL_n(Z).
We show that the ring of multiplicative invariants
k[x_1, 1/x_1, \dots, x_n, 1/x_n]^G has a finite SAGBI basis if
and only if G is generated by reflections.

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