Krull–Gabriel dimension and the model-theoretic complexity of the category of modules over group rings of finite groups

Puninski, Gena; Puninskaya, Vera; Toffalori, Carlo
August 2008
Journal of the London Mathematical Society;Aug2008, Vol. 78 Issue 1, p125
Academic Journal
We classify group rings of finite groups over a field F according to the model-theoretic complexity of the category of their modules. For instance, we prove that, if F contains a primitive cubic root of 1, then the Krull–Gabriel dimension of such rings is 0, 2, or undefined.


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