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Abstract
In this article, we study various homological invariants of differential graded (DG for short) modules over a connected DG algebra following Frankild–Jørgensen. Two different versions of homological dimensions (resolutional and functorial) are defined. In some cases, they are proved to be simply the bound of the cohomology of the DG module. Some homological identities, such as Auslander–Buchsbaum formula and Bass formula, are proved for compact DG modules over a connected DG algebra.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The authors thank the referee for his (her) valuable comments and suggestions. This research is supported by the NSFC (key project 10331030) and supported by the Cultivation Fund of the Key Scientific and Technical Innovation Project (No. 704004), Doctorate Foundation (No. 20060246003), Ministry of Education of China.
Notes
Communicated by J. Kuzmanovich.