Skip to main content
×
Home
    • Aa
    • Aa

Some properties of non-commutative regular graded rings

  • Thierry Levasseur (a1)
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

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Some properties of non-commutative regular graded rings
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Some properties of non-commutative regular graded rings
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Some properties of non-commutative regular graded rings
      Available formats
      ×
Copyright
Linked references
Hide All

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×