Krull, Gelfand–Kirillov, and Filter Dimensions of Simple Affine Algebras

The aim of the paper is to prove the following two results. 1. LetAbe a finitely partitive simple affine algebra with GK(A) < ∞. Then the Krull dimension, where GK and fil.dim are the Gelfand–Kirillov and the filter dimension, respectively. 2. LetBbe an integral regular domain, affine over a field of characteristic zero and let (B) be its ring of differential operators. The filter dimension fil.dim (B) = 1.