Let G be an affine algebraic group with a reductive identity component G⁰ acting regularly on an affine Krull scheme X = Spec(R) over an algebraically closed field. Let T be an algebraic subtorus of G and suppose that  of quotient fields. We will show: If G is the centralizer of T in G, then the pseudo-reflections of the action of G on R^T can be lifted to those on R. This result is applied to partially generalize Chevalley-Serre and Steinberg theorems on pseudo-reflection groups.

algebraic torus, pseudo-reflection, Krull domain, ramification index, invariant theory.