We provide an introduction to the the Krull-Gabriel dimension of a ring, as well as many related ideas. In particular, we outline how Krull-Gabriel dimension relates to the Cantor-Bendixson rank of the Ziegler spectrum and with the Jacobson radical of the module category. We also include a list of examples of rings and categories where the Krull-Gabriel dimension has been calculated.
Krull-gabriel dimension and the ziegler spectrum
Laking R.
2018-01-01
Abstract
We provide an introduction to the the Krull-Gabriel dimension of a ring, as well as many related ideas. In particular, we outline how Krull-Gabriel dimension relates to the Cantor-Bendixson rank of the Ziegler spectrum and with the Jacobson radical of the module category. We also include a list of examples of rings and categories where the Krull-Gabriel dimension has been calculated.
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