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Abstract:
The study of Gorenstein dimensions was initiated in the 1960's by Auslander and Bridger.
These relative homological dimensions can be considered as "refinements" of the classical
homological dimensions and are closely related to the class of commutative Gorenstein rings.
In fact, finiteness of Gorenstein dimensions characterizes Gorenstein rings in a similar
way that finiteness of classical homological dimensions characterizes regular rings. InÊ
this talk, we will try to give an overview of the theory by reviewing the fundamental
definitions and properties of Gorenstein dimensions as well asÊrecent developments in the
theory.
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