Frontiers of Mathematics in China >

2021 , Vol. 16 >Issue 1: 95 - 117

DOI: https://doi.org/10.1007/s11464-021-0887-8

RESEARCH ARTICLE

Proper resolutions and Gorensteinness in extriangulated categories

  • Jiangsheng HU 1 ,
  • Dondong ZHANG , 2 ,
  • Panyue ZHOU 3
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  • 1. Department of Mathematics, Jiangsu University of Technology, Changzhou 213001, China
  • 2. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
  • 3. College of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China

Received date: 20 Jan 2020

Accepted date: 16 Dec 2020

Published date: 15 Feb 2021

Copyright

2021 Higher Education Press
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Abstract

Let (ℓ,E,s) be an extriangulated category with a proper class ξ of E-triangles, and W an additive full subcategory of (ℓ,E,s). We provide a method for constructing a proper Wξ-resolution (resp., coproper Wξ- coresolution) of one term in an E-triangle in ξ from that of the other two terms. By using this way, we establish the stability of the Gorenstein category GWξ in extriangulated categories. These results generalize the work of Z. Y. Huang [J. Algebra, 2013, 393: 142{169] and X. Y. Yang and Z. C. Wang [Rocky Mountain J. Math., 2017, 47: 1013{1053], but the proof is not too far from their case. Finally, we give some applications about our main results.

Key words： Proper resolution; coproper coresolution; extriangulated categories; Gorenstein categories

Cite this article

Jiangsheng HU , Dondong ZHANG , Panyue ZHOU . Proper resolutions and Gorensteinness in extriangulated categories[J]. Frontiers of Mathematics in China, 2021 , 16(1) : 95 -117 . DOI: 10.1007/s11464-021-0887-8

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