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On Modules M such that both M and M∗ are Semi-Gorenstein-Projective

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Abstract

Let A be an artin algebra. An A-module M is semi-Gorenstein-projective provided that Exti(M,A) = 0 for all i ≥ 1. If M is Gorenstein-projective, then both M and its A-dual M∗ are semi-Gorenstein projective. As we have shown recently, the converse is not true, thus answering a question raised by Avramov and Martsinkovsky. The aim of the present note is to analyse in detail the modules M such that both M and M∗ are semi-Gorenstein-projective.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, 33501, Bielefeld, Germany

    Claus Michael Ringel

  2. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Pu Zhang

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  1. Claus Michael Ringel
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  2. Pu Zhang
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Correspondence to Claus Michael Ringel or Pu Zhang.

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Presented by: Michel Brion

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Ringel, C.M., Zhang, P. On Modules M such that both M and M∗ are Semi-Gorenstein-Projective. Algebr Represent Theor 24, 1125–1140 (2021). https://doi.org/10.1007/s10468-020-09982-w

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  • DOI: https://doi.org/10.1007/s10468-020-09982-w

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