Czechoslovak Mathematical Journal, online first, 18 pp.

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

Chao Wang, Xiaoyan Yang

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

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

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 2010): 18G25, 16E65, 18E30

DOI: 10.21136/CMJ.2017.0346-16

Full text available as PDF.


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