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Symmetry of self-injective dimensions under the Auslander condition
Abstract
Let A be a module-finite algebra over a commutative Noetherian ring. We give a local criterion for the n-Gorenstein condition. For such algebras satisfying the Auslander condition, we prove that finite self-injective dimension is symmetric. Under a one-sided local finiteness hypothesis, we further characterize the Auslander condition by a fiberwise form of Iyama's grade bijection and obtain a criterion for the Auslander--Gorenstein property.
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BibTeX
@misc{shen2026symmetry,
title = {{Symmetry of self-injective dimensions under the Auslander condition}},
author = {Dawei Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.15974},
eprint = {2608.15974},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15974},
}
RIS
TY - UNPB
TI - Symmetry of self-injective dimensions under the Auslander condition
AU - Dawei Shen
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2608.15974
UR - https://arxiv.org/abs/2608.15974
AB - Let A be a module-finite algebra over a commutative Noetherian ring. We give a local criterion for the n-Gorenstein condition. For such algebras satisfying the Auslander condition, we prove that finite self-injective dimension is symmetric. Under a one-sided local finiteness hypothesis, we further characterize the Auslander condition by a fiberwise form of Iyama's grade bijection and obtain a criterion for the Auslander--Gorenstein property.
ER -