Finiteness of finitistic dimension is invariant under derived equivalences. (English) Zbl 1172.16007
Summary: We show that the finiteness of the finitistic dimension of a left coherent ring is invariant under derived equivalences.
MSC:
16E10 | Homological dimension in associative algebras |
18E30 | Derived categories, triangulated categories (MSC2010) |
16G10 | Representations of associative Artinian rings |
16E30 | Homological functors on modules (Tor, Ext, etc.) in associative algebras |
References:
[1] | Broué, M., Equivalences of blocks of group algebras, (Dlab, V.; Scott, L. L., Finite Dimensional Algebras and Related Topics (1994), Kluwer), 1-26 · Zbl 0827.20007 |
[2] | Dugger, D.; Shipley, B., K-theory and derived equivalences, Duke Math. J., 124, 3, 587-617 (2004) · Zbl 1056.19002 |
[3] | Happel, D., Reduction techniques for homological conjectures, Tsukuba J. Math., 17, 1, 115-130 (1993) · Zbl 0809.16021 |
[4] | Happel, D., Triangulated Categories in the Representation Theory of Finite Dimensional Algebras (1988), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0635.16017 |
[5] | Hu, W.; Xi, C. C., Almost \(D\)-split sequences and derived equivalences (2007), Preprint, available at: |
[6] | Kato, Y., On derived equivalent coherent rings, Comm. Algebra, 30, 9, 4437-4454 (2002) · Zbl 1030.16002 |
[7] | Rickard, J., Morita theory for derived categories, J. London Math. Soc., 39, 436-456 (1989) · Zbl 0642.16034 |
[8] | Rickard, J., Derived equivalences as derived functors, J. London Math. Soc., 43, 37-48 (1991) · Zbl 0683.16030 |
[9] | Xi, C. C.; Xu, D. M., The finitistic dimension conjecture and relatively projective modules (2007), Preprint, available at: |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.