Illinois Journal of Mathematics

Thick subcategories and virtually Gorenstein algebras

Apostolos Beligiannis and Henning Krause

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An Artin algebra is by definition virtually Gorenstein if the class of modules which are right orthogonal (with respect to $\operatorname {Ext}^*(-,-)$) to all Gorenstein projective modules coincides with the class of modules which are left orthogonal to all Gorenstein injective modules. We provide a new characterization in terms of finitely generated modules. In addition, an example of an algebra is presented which is not virtually Gorenstein.

Article information

Illinois J. Math., Volume 52, Number 2 (2008), 551-562.

First available in Project Euclid: 23 July 2009

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Zentralblatt MATH identifier

Primary: 16G50: Cohen-Macaulay modules
Secondary: 18E30: Derived categories, triangulated categories 16E65: Homological conditions on rings (generalizations of regular, Gorenstein, Cohen-Macaulay rings, etc.)


Beligiannis, Apostolos; Krause, Henning. Thick subcategories and virtually Gorenstein algebras. Illinois J. Math. 52 (2008), no. 2, 551--562. doi:10.1215/ijm/1248355349.

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