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Graded rings ofcohomological dimension 2

Published online by Cambridge University Press:  13 November 2000

Q. S. Wu  and
J. J. Zhang
Q. S. Wu
Affiliation:
Institute of Mathematics, Fudan University, Shanghai, 200433, China. E-mail: cwu@math.washington.edu, qswu@fudan.edu.cn
J. J. Zhang
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, USA. E-mail: zhang@math.washington.edu
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Abstract

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Let A be a noetherian connected graded ring with a balanced dualizing complex R. If A has cohomological dimension and Krull dimension 2, then

(1) R is Auslander;

(2) \rm{Cdim} M=\rm{Kdim} M for all noetherian graded A-modules M.

In particular, ifA is AS-Gorenstein of injective and Krull dimension 2, then

(3)A is Auslander-Gorenstein;

(4) A is 2-pure with a self-injective artinian quotient ring;

(5) A has a residue complex.

(1,3,4) generalize a result of Levasseur [7, 5.13] and (5) generalizes a result of Ajitabh [1, 3.12].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 3 , September 2000 , pp. 455 - 468
Copyright
2000 Glasgow Mathematical Journal Trust