Czechoslovak Mathematical Journal, Vol. 67, No. 4, pp. 1031-1048, 2017


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

Chao Wang, Xiaoyan Yang

Received July 1, 2016.  First published March 1, 2017.

Abstract:  Let $\Lambda=\left(\begin{smallmatrix} A&M 0&B \end{smallmatrix}\right)$ be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective $\Lambda$-modules under the condition that $M$ is a cocompatible $(A,B)$-bimodule, we establish a recollement of the stable category $\overline{\rm Ginj(\Lambda)}$. We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over $\Lambda$.
Keywords:  (strongly) Gorenstein injective module; upper triangular matrix Artin algebra; triangulated category; recollement
Classification MSC:  18G25, 16E65, 18E30
DOI:  10.21136/CMJ.2017.0346-16

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Affiliations:   Chao Wang (corresponding author), Xiaoyan Yang, Department of Mathematics, Northwest Normal University, Anning East Road No. 967, Lanzhou, 730070, Gansu, P. R. China, e-mail: wangchao0314math@163.com, yangxy@nwnu.edu.cn

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