G-dimension, complete intersection dimension, complexity, and relative homological algebra. (English) Zbl 0987.13005
The aim of the paper is to give new views on the concepts of \(G\)-dimension and \(CI\)-dimension, notions that played big roles in recent researches in homological and commutative algebra. It is shown that these concepts can be treated as relative projective dimensions for suitably chosen classes of relatively projective modules. A notion of relative depth is introduced and its properties are studied, including Auslander-Buchsbaum formulas. A new cohomology theory, similar to Vogel’s generalization of Tate cohomology is constructed, characterizing this time complete intersections instead of regular local rings, is constructed. Ideas for further research are considered.
Reviewer: Christodor-Paul Ionescu (Bucureşti)
MSC:
| 13D05 | Homological dimension and commutative rings |
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