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Krull–Gabriel dimension and the model‐theoretic complexity of the category of modules over group rings of finite groups
Author(s) -
Puninski Gena,
Puninskaya Vera,
Toffalori Carlo
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdn015
Subject(s) - krull dimension , mathematics , dimension (graph theory) , group (periodic table) , pure mathematics , combinatorics , discrete mathematics , algebra over a field , physics , noetherian , quantum mechanics
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.