In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Λ be an Artin algebra and M a Λ -generator such that ExtΛi (M, M) = 0 for all i ≥ 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen-Macaulay normal domains containing the rational numbers, and slightly more generally.
ASJC Scopus subject areas
- Algebra and Number Theory