Derivations and root closures of graded ideals

Abstract

We show that the graded structure of an ideal is preserved under root closures. As an application, for a locally nilpotent derivation [Formula: see text] on a Noetherian integral domain [Formula: see text] containing a field of characteristic zero, we show that if [Formula: see text] is [Formula: see text]-invariant, then so are its root closures.