163
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

On G-Regular Local Rings

Pages 4472-4491 | Received 21 Aug 2007, Published online: 12 Dec 2008

REFERENCES

  • Auslander , M. ( 1967 ). Anneaux de Gorenstein, et torsion en algèbre commutative. Séminaire d'Algèbre Commutative dirigé par Pierre Samuel, 1966/67, Texte rédigé, d'après des exposés de Maurice Auslander, Marquerite Mangeney, Christian Peskine et Lucien Szpiro. École Normale Supérieure de Jeunes Filles , Secrériat Mathétique , Paris .
  • Auslander , M. , Bridger , M. (1969). Stable Module Theory. Memoirs of the American Mathematical Society . No. 94, Providence , RI : American Mathematical Society.
  • Avramov , L. L. ( 1998 ). Infinite free resolutions . In: Six Lectures on Commutative Algebra (Bellaterra, 1996). Progr. Math., 166 , Basel : Birkhäuser , pp. 1 – 118 .
  • Avramov , L. L. ( 2002 ). Homological dimensions and related invariants of modules over local rings . In: Representations of Algebra . Vols. I, II , Beijing : Beijing Norm. Univ. Press , pp. 1 – 39 .
  • Avramov , L. L. , Martsinkovsky , A. ( 2002 ). Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension . Proc. London Math. Soc. (3) 85 ( 2 ): 393 – 440 .
  • Bourbaki , N. ( 1998 ). Commutative Algebra . Chapters 1–7. Translated from the French. Reprint of the 1989 English translation. Elements of Mathematics (Berlin) . Berlin : Springer-Verlag .
  • Bruns , W. , Herzog , J. ( 1998 ). Cohen–Macaulay Rings . Revised edition. Cambridge Studies in Advanced Mathematics, 39 , Cambridge : Cambridge University Press .
  • Christensen , L. W. ( 2000 ). Gorenstein Dimensions . Lecture Notes in Mathematics, 1747 . Berlin : Springer-Verlag .
  • Christensen , L. W. , Piepmeyer , G. , Striuli , J. , Takahashi , R. ( 2008 ). Finite Gorenstein representation type implies simple singularity . Adv. Math. 218 ( 4 ): 1012 – 1026 .
  • Eisenbud , D. ( 1980 ). Homological algebra on a complete intersection, with an application to group representations . Trans. Amer. Math. Soc. 260 ( 1 ): 35 – 64 .
  • Knörrer , H. ( 1987 ). Cohen–Macaulay modules on hypersurface singularities. I . Invent. Math. 88 ( 1 ): 153 – 164 .
  • Matsumura , H. ( 1980 ). Commutative Algebra. , 2nd ed . Mathematics Lecture Note Series, 56 . Reading, Mass .: Benjamin/Cummings Publishing Co., Inc. .
  • Takahashi , R. ( 2004a ). On the category of modules of Gorenstein dimension zero. II . J. Algebra 278 ( 1 ): 402 – 410 .
  • Takahashi , R. ( 2004b ). Modules of G-dimension zero over local rings of depth two . Illinois J. Math. 48 ( 3 ): 945 – 952 .
  • Takahashi , R. ( 2005 ). On the category of modules of Gorenstein dimension zero . Math. Z. 251 ( 2 ): 249 – 256 .
  • Takahashi , R. ( 2006 ). Remarks on modules approximated by G-projective modules . J. Algebra 301 ( 2 ): 748 – 780 .
  • Takahashi , R. ( 2007a ). On the number of indecomposable totally reflexive modules . Bull. London Math. Soc. 39 ( 3 ): 487 – 492 .
  • Takahashi , R. ( 2007b ). An uncountably infinite number of indecomposable totally reflexive modules . Nagoya Math. J. 187 : 35 – 48 .
  • Takahashi , R. , Watanabe , K.-i . ( 2007 ). Totally reflexive modules constructed from smooth projective curves of genus g ≥ 2 . Arch. Math. (Basel) 89 ( 1 ): 60 – 67 .
  • Tate , J. ( 1957 ). Homology of Noetherian rings and local rings . Illinois J. Math. 1 : 14 – 27 .
  • Yoshino , Y. ( 1990 ). Cohen–Macaulay Modules Over Cohen–Macaulay Rings . London Mathematical Society Lecture Note Series, 146 . Cambridge : Cambridge University Press .
  • Yoshino , Y. ( 2003 ). Modules of G-dimension zero over local rings with the cube of maximal ideal being zero . In: Commutative Algebra, Singularities and Computer Algebra (Sinaia, 2002). NATO Sci. Ser. II Math. Phys. Chem., 115 . Dordrecht : Kluwer Acad. Publ. , pp. 255 – 273 .
  • Communicated by I. Swanson.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.