On the stratification of noncommutative prime spectra

We study rational actions of an algebraic torus G by automorphisms on an associative algebra R. The G-action on R induces a stratification of the prime spectrum of R which was introduced by Goodearl and Letzter. For a noetherian algebra R, Goodearl and Letzter showed that the strata of the spectrum of R are isomorphic to the spectra of certain commutative Laurent polynomial algebras. The purpose of this note is to give a new proof of this result which works for arbitrary algebras R.