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Construction of Modules with Finite Homological Dimensions

✍ Scribed by Oana Veliche

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
163 KB
Volume
250
Category
Article
ISSN
0021-8693

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✦ Synopsis

A new homological dimension, called G * -dimension, is defined for every finitely generated module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov, Gasharov, and Peeva and has parallel properties. In particular, a ring R is Gorenstein if and only if every finitely generated R-module has finite G * -dimension. The G * -dimension lies between the CI-dimension and the G-dimension of Auslander and Bridger. This relation belongs to a longer sequence of inequalities, where a strict inequality in any place implies equalities to its right and left. Over general local rings, we construct classes of modules that show that a strict inequality can occur at almost every place in the sequence.  2002 Elsevier Science (USA)

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