Abstract:
Let R be an algebra, and let (theta, <=) be a stratifying system of R-modules. If the category) F(theta) is theta-directing, then we prove that ind F(theta) is finite. In order to do that, we introduce a quadratic form q(theta) which depends on theta. Moreover, we also give sufficient conditions to get the correspondence X -> dim(theta)X from ind F(theta) to the set of positive roots of q(theta). (c) 2006 Elsevier Inc. All rights reserved.