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Preprint Number 50

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50. Gena Puninski, Vera Puninskaya, Carlo Toffalori
Krull-Gabriel dimension and the model-theoretic complexity of the category of modules over group rings of finite groups
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Submission date: 30 January 2007

Abstract:

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.

Mathematics Subject Classification: 03C60, 16D50, 16S34, 16G30

Keywords and phrases: Krull-Gabriel dimension, width, group rings of finite groups

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