Abstract
This article is a report of three lectures given on “Dimension Theory of Noetherian Rings”, at the meeting “Infinite Length Modules”, held in Bielefeld, from 7th to 11th September 1998. I would like to thank the organisers for the opportunity to present these lectures, and for the invitation to write up the lectures for this volume. I was asked to present an introduction to the uses of dimension theory in noetherian rings for an audience of algebraists who were not specialists in the area of noetherian rings. In view of this, the material presented here is not original work, nor is it necessarily the most important work in this area. Rather, the results and examples were chosen to illustrate typical uses of dimension theory. Since most of the audience consisted of experts in the Representation theory of Artin rings and finite dimensional algebras, I decided to concentrate on two dimension functions, Krull dimension and Gelfand-Kirillov dimension, which are generalisations of the notions of artinian and finite dimensional, respectively.
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Lenagan, T.H. (2000). Dimension Theory of Noetherian Rings. In: Krause, H., Ringel, C.M. (eds) Infinite Length Modules. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8426-6_6
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