Illinois Journal of Mathematics

Two generalizations of Auslander–Reiten duality and applications

Arash Sadeghi and Ryo Takahashi

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This paper extends Auslander–Reiten duality in two directions. As an application, we obtain various criteria for freeness of modules over local rings in terms of vanishing of Ext modules, which recover a lot of known results on the Auslander–Reiten conjecture.

Article information

Illinois J. Math., Volume 63, Number 2 (2019), 335-351.

Received: 9 January 2019
Revised: 22 April 2019
First available in Project Euclid: 1 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13C14: Cohen-Macaulay modules [See also 13H10] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]


Sadeghi, Arash; Takahashi, Ryo. Two generalizations of Auslander–Reiten duality and applications. Illinois J. Math. 63 (2019), no. 2, 335--351. doi:10.1215/00192082-7768744.

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