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Totally acyclic complexes and locally Gorenstein rings

Lars Winther Christensen

Texas Tech University, Lubbock, TX 79409, USA

E-mail Address: lars.w.christensen@ttu.edu

Corresponding author.

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and

Kiriko Kato

Osaka Prefecture University, Sakai, Osaka 599-8531, Japan

E-mail Address: kiriko@mi.s.osakafu-u.ac.jp

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https://doi.org/10.1142/S0219498818500391Cited by:2 (Source: Crossref)

Abstract

A commutative noetherian ring with a dualizing complex is Gorenstein if and only if every acyclic complex of injective modules is totally acyclic. We extend this characterization, which is due to Iyengar and Krause, to arbitrary commutative noetherian rings, i.e. we remove the assumption about a dualizing complex. In this context Gorenstein, of course, means locally Gorenstein at every prime.

Communicated by R. Wiegand

Keywords:

AMSC: 13D02, 13H10

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