Illinois Journal of Mathematics

Two generalizations of Auslander–Reiten duality and applications

Arash Sadeghi and Ryo Takahashi

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1564646438

Digital Object Identifier
doi:10.1215/00192082-7768744

Mathematical Reviews number (MathSciNet)
MR3987500

Zentralblatt MATH identifier
07088310

Subjects
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]

Citation

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. https://projecteuclid.org/euclid.ijm/1564646438


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