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Some properties of non-commutative regular graded rings

  • Thierry Levasseur (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500008843
  • Published online: 01 May 2009
Abstract

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

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.M. Artin and W. F. Schelter , Graded algebras of global dimension 3, Adv. in Math. 66 (1987), 171216.

3.M. Artin , J. Tate and M. Van den Bergh , Some algebras associated to automorphisms of elliptic curves, The Grothendieck Festschrift (Birkhauser, 1990), 3385.

5.M. Artin and M. Van den Bergh , Twisted homogeneous coordinate rings, Algebra 133 (1990), 249271.

12.F. Ischebeck , Eine Dualität Zwischen den Funktoren Ext und Tor, J. Algebra 11 (1969), 510531.

14.T. Levasseur , Complexe bidualisant en algèbre non commutative, Séminaire Dubreil-Malliavin 1983–84, Lecture Notes in Mathematics 1146 (Springer, 1985), 270287.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
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