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

Chao Wang; Xiao Yan Yang

Czechoslovak Mathematical Journal (2017)

  • Volume: 67, Issue: 4, page 1031-1048
  • ISSN: 0011-4642

Abstract

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Let Λ = A M 0 B 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 Ginj ( Λ ) ¯ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ .

How to cite

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Wang, Chao, and Yang, Xiao Yan. "(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras." Czechoslovak Mathematical Journal 67.4 (2017): 1031-1048. <http://eudml.org/doc/294630>.

@article{Wang2017,
abstract = {Let $\Lambda =\left(\{\{\textstyle \begin\{matrix\} A&M\\ 0&B \end\{matrix\}\}\}\right)$ 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 $.},
author = {Wang, Chao, Yang, Xiao Yan},
journal = {Czechoslovak Mathematical Journal},
keywords = {(strongly) Gorenstein injective module; upper triangular matrix Artin algebra; triangulated category; recollement},
language = {eng},
number = {4},
pages = {1031-1048},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras},
url = {http://eudml.org/doc/294630},
volume = {67},
year = {2017},
}

TY - JOUR
AU - Wang, Chao
AU - Yang, Xiao Yan
TI - (Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 4
SP - 1031
EP - 1048
AB - Let $\Lambda =\left({{\textstyle \begin{matrix} A&M\\ 0&B \end{matrix}}}\right)$ 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 $.
LA - eng
KW - (strongly) Gorenstein injective module; upper triangular matrix Artin algebra; triangulated category; recollement
UR - http://eudml.org/doc/294630
ER -

References

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