43
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Weakly GK-Perfect and Integral Closure of Ideals

, &
Pages 4500-4508 | Received 25 Sep 2007, Published online: 12 Dec 2008

REFERENCES

  • Auslander , M. ( 1967 ). Anneaux de Gorenstein et Torsion en Algèbre Commutative . Séminaire d'algèbre commutative 1966/67, notes by Mangeney, M., Peskine, C., Szpiro, L., École Normale Supérieure de Jeunes Filles, Paris .
  • Auslander , M. , Bridger , M. ( 1969 ). Stable module theory . Mem. Amer. Math. Soc. 94 .
  • Brodmann , M. P. , Sharp , R. Y. ( 1998 ). Local Cohomology: An Algebraic Introduction with Geometric Applications . Cambridge : Cambridge University Press .
  • Bruns , W. , Herzog , J. ( 1998 ). Cohen–Macaulay Rings . Cambridge Studies in Advanced Mathematics . Vol. 39 , Cambridge , UK : Cambridge Univ. Press .
  • Divaani-Aazar , K. , Naghipour , R. , Tousi , M. (2002). Cohomological dimension of certain algebraic varieties. Proc. Amer. Math. Soc. 130:3537–3544.
  • Foxby , H.-B . ( 1972 ). Gorenstein modules and related modules . Math. Scand. 31 : 267 – 284 .
  • Foxby , H.-B . ( 1975 ). Quasi-perfect modules over Cohen–Macaulay rings . Math. Nachr. 66 : 103 – 110 .
  • Gerko , A. A. ( 2001 ). On homological dimensions . Translation in Sb. Math. 192 ( 7–8 ): 1165 – 1179 .
  • Golod , E. S. ( 1985 ). G-dimension and generalized perfect ideals . English Transl. in Proc. Steclov Inst. Math. 165 : 67 – 71 .
  • Goto , S. ( 1987 ). Integral closedness of complete-intersection ideals . J. Algebra 108 : 151 – 160 .
  • Goto , S. , Hayasaka , F. ( 2002 ). Finite homological dimension and primes associated to integrally closed ideals . Proc. Amer. Math. Soc. 130 : 3159 – 3164 .
  • Grothendieck , A. ( 1967 ). Local Cohomology . Lecture Notes in Mathematics, 41 , Berlin : Springer .
  • Huneke , C. ( 1992 ). Problems on local cohomology, Free resolutions in commutative algebra and algebraic geometry . Res. Notes Math. 2 : 93 – 108 .
  • Matsumura , H. ( 1986 ). Commutative Ring Theory . Cambridge , UK : Cambridge Univ. Press .
  • Northcott , D. G. , Rees , D. ( 1954 ). Reduction of ideals in local rings . Proc. Cambridge Philos. Soc. 50 : 145 – 158 .
  • Rotman , J. ( 1979 ). An Introduction to Homological Algebra . San Diego : Academic Press .
  • Sharp , R. Y. ( 1998 ). Linear growth of primary decompositions of integral closures of ideals . J. Algebra 207 : 276 – 284 .
  • Takahashi , R. ( 2006 ). Syzygy modules with semidualizing or G-projective summands . J. Algebra 295 : 179 – 194 .
  • Communicated by S. Goto.

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.