Lifting group representations to maximal Cohen-Macaulay representations. (English) Zbl 0896.16008
This work generalizes some of M. Auslander’s and S. O. Smalø’s work [J. Algebra 66, No. 1, 61-122 (1980; Zbl 0477.16013)] on existence of Cohen-Macaulay approximations.
In the first section the authors show that the existence of a Matlis dualizing module for a ring \(R\) implies the same existence for the group ring \(RG\) if \(G\) is a finite group. The Gorenstein case is studied in section 2. In the last section the results are applied to give a generalization of the Teichmüller invariants.
In the first section the authors show that the existence of a Matlis dualizing module for a ring \(R\) implies the same existence for the group ring \(RG\) if \(G\) is a finite group. The Gorenstein case is studied in section 2. In the last section the results are applied to give a generalization of the Teichmüller invariants.
Reviewer: E.Marcos (São Paulo)
MSC:
| 16E10 | Homological dimension in associative algebras |
| 14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
| 16G50 | Cohen-Macaulay modules in associative algebras |
| 16S34 | Group rings |
Keywords:
Cohen-Macaulay approximations; Gorenstein rings; Teichmüller invariants; Matlis dualizing modules; group ringsCitations:
Zbl 0477.16013References:
| [1] | M. Auslander, Minimal Cohen-Macaulay approximations; M. Auslander, Minimal Cohen-Macaulay approximations · Zbl 0697.13005 |
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| [3] | Auslander, M.; Buchweitz, R. O., Maximal Cohen-Macaulay approximations, Mém. Soc. Math. France (N.S.), 38, 5-37 (1989) · Zbl 0697.13005 |
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