KRULL, GELFAND-KIRILLOV, AND FILTER DIMENSIONS OF SIMPLE AFFINE ALGEBRAS

The aim of the paper is to prove the following two results. 1. Let A b e a finitely partitive simple affine algebra with GR(A) < infinity. Th en the Krull dimension, K.dim(A) less than or equal to GK(A) {1 - 1/fi l.dim A + max{fil.dim A, 1}}, where GK and fil.dim are the Gelfand-Kir illov and the filter dimension, respectively. 2. Let B be an integral regular domain, affine over a field of characteristic zero and let D(B ) be its ring of differential operators. The filter dimension fil.dim D(B) = 1. (C) 1998 Academic Press.