On a conjecture of Auslander and Reiten

Craig Huneke; Graham J. Leuschke

doi:10.1016/j.jalgebra.2003.07.018

On a conjecture of Auslander and Reiten

Craig Huneke, Graham J. Leuschke

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

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_Λⁱ (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.

Original language	English (US)
Pages (from-to)	781-790
Number of pages	10
Journal	Journal of Algebra
Volume	275
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2003.07.018
State	Published - May 15 2004
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2003.07.018

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title = "On a conjecture of Auslander and Reiten",

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 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.",

author = "Craig Huneke and Leuschke, {Graham J.}",

note = "Funding Information: * Corresponding author. Present address: Department of Mathematics, University of Toronto, Toronto, ON, Canada M5S 3G3. E-mail addresses: [email protected] (C. Huneke), [email protected] (G.J. Leuschke). URLs: http://www.math.ukans.edu/~huneke, http://www.leuschke.org/. 1 The author was supported by NSF grant DMS-0098654. 2 The author was supported by an NSF Postdoctoral Fellowship and the Clay Mathematics Institute.",

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N2 - 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.

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On a conjecture of Auslander and Reiten

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