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Recollement ideals and recollements of Gorenstein defect categories
Electronic Research Archive 2026, 34(4): 2348-2363
Published: 15 April 2026
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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.

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