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- Title
The Finitistic Dimension and Global Dimension of an Artinian Ring with a Dualizing Complex.
- Authors
Zhang, Yaohua
- Abstract
Let R be an Artinian ring with a dualizing complex D•. Then (1) if the injective modules generate the derived category D (R) as a triangulated category with arbitrary coproducts, then the finitistic dimension of R is finite; (2) if the injective modules generate the homotopy category K (R − lnj) as a triangulated category with arbitrary coproducts, then the global dimension of R is finite. The first result generalizes Theorem 4.3 in [Adv. Math., 2019, 354: 106735, 21 pp.].
- Subjects
TRIANGULATED categories; ARTIN rings; GORENSTEIN rings; MATHEMATICS
- Publication
Frontiers of Mathematics, 2023, Vol 18, Issue 4, p953
- ISSN
2731-8648
- Publication type
Article
- DOI
10.1007/s11464-020-0169-x