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Some properties of non-commutative regular graded rings

Published online by Cambridge University Press:  18 May 2009

Thierry Levasseur
Thierry Levasseur
Affiliation:
Département de Mathématiques, Université de Bretagne Occidentale, 6, Avenue Victor Le Gorgeu, 29287 Brest Cedex, France
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Let A be a noetherian ring. When A is commutative (of finite Krull dimension), A is said to be Gorenstein if its injective dimension is finite. If A has finite global dimension, one says that A is regular. If A is arbitrary, these hypotheses are not sufficient to obtain similar results to those of the commutative case. To remedy this problem, M. Auslander has introduced a supplementary condition. Before stating it, we recall that the grade of a finitely generated (left or right) module is defined by

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 277 - 300
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

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