ON A CONJECTURE OF AUSLANDER AND REITEN

By Craig Huneke, Graham J. Leuschke. 2003

60 citations recorded by the source corpus.

Abstract 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 Ext i Λ ( 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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/e44495d2f3ef2b0462f22b78b21fa2ad132646be

Citations in the corpus

• Algebras that satisfy Auslander’s condition on vanishing of cohomology (2008, unknown): “[8,24,25,38].”