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Research Article | Open Access

Recollement ideals and recollements of Gorenstein defect categories

Huanhuan Li1, Hanyang You2,3( ), Yuefei Zheng4, Haiyan Zhu5
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
College of Science, Shanghai University, Shanghai 200444, China
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
College of Science, Northwest A&F University, Yangling 712100, China
College of Science, Zhejiang University of Technology, Hangzhou 310000, China
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Abstract

Let R be an Artin algebra and e ∈ R an idempotent. We study when the recollement ideal R e R induces (left) recollement of Gorenstein defect categories. As a consequence of this phenomenon, concrete triangle-equivalences between Gorenstein defect categories (resp. stable categories of Gorenstein projective modules) of R and R / R e R (resp. e R e) are obtained, and reduction conditions for Gorensteinness (resp. CM-freeness) of R and Gorenstein projective conjecture over R are provided. Finally, some applications in the context of triangular matrix algebras are given.

Keywords

recollementsrecollement idealsGorenstein projective modulesGorenstein defect categoriesGorenstein projective conjecture

References

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Electronic Research Archive
Volume 34 Issue 4,
April 2026
Pages 2348-2363
DOI: 10.3934/era.2026106

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Cite this article:
Li H, You H, Zheng Y, et al. Recollement ideals and recollements of Gorenstein defect categories. Electronic Research Archive, 2026, 34(4): 2348-2363. https://doi.org/10.3934/era.2026106

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Received: 03 December 2025
Revised: 27 February 2026
Accepted: 03 March 2026
Published: 15 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)