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FP-injective dimensions and Gorenstein homology

Part of: Homological algebra

Published online by Cambridge University Press:  21 December 2022

Gang Yang  and
Junpeng Wang
Gang Yang
Affiliation:
Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China (yanggang@mail.lzjtu.cn)
Junpeng Wang*
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China (wangjunpeng1218@163.com)
*
*Corresponding author
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Abstract

Let $R$ be a left coherent ring. It is proven that if an $R$-module $M$ has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\mathcal {GP},\, \mathcal {GP}^{\perp }$) forms a projective cotorsion pair under some mild conditions.

Keywords

FP-injective modulesGorenstein projective modulesGorenstein flat modules

MSC classification

Primary: 18G25: Relative homological algebra, projective classes
Secondary: 18G20: Homological dimension
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 65 , Issue 4 , November 2022 , pp. 1183 - 1199
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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