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(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

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Abstract

Let \(\Lambda = \left( {\begin{array}{*{20}{c}} A&M \\ 0&B \end{array}} \right)\) be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ-modules under the condition that M is a cocompatible (A,B)-bimodule, we establish a recollement of the stable category \(\overline {Ginj\left( \Lambda \right)} \). We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ.

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Authors and Affiliations

  1. Department of Mathematics, Northwest Normal University, Anning East Road No. 967, Lanzhou, Gansu, 730070, P.R. China

    Chao Wang & Xiaoyan Yang

Authors
  1. Chao Wang
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  2. Xiaoyan Yang
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Corresponding author

Correspondence to Chao Wang.

Additional information

This research was partially supported by the Program for New Century Excellent Talents in University (NCET-13-0957) and NSFC (11361051, 11361052).

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Wang, C., Yang, X. (Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras. Czech Math J 67, 1031–1048 (2017). https://doi.org/10.21136/CMJ.2017.0346-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0346-16

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