On the polynomiality of invariant rings for codimension one Ga-modules

Let k be an algebraically closed field of positive characteristic and let Ga be its additive group. Let Ga act linearly on a finite-dimensional vector space V, let k[V] be the ring of polynomial functions on V, and let kGa[V] be the ring of Ga-invariants. In this article, we show that the ring of Ga-invariants kGa[V] is a polynomial ring under the assumption that V is a codimension one Ga-module.