79
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

On the Comparison of Rees's Valuations Over a Quasi-Unmixed Local Ring

Pages 4671-4678 | Received 29 Oct 2012, Published online: 23 May 2014

REFERENCES

  • Beddani , C. ( 2009 ). Clôture intégrale des idéaux et la propriété (Z k ) . Communications in Algebra 37 : 4079 – 4094 .
  • Beddani , C. ( 2013 ). On the integral closure of ideals satisfying the condition (C 2) . Journal of Algebra and Its Applications 12 ( 6 ): 1350006-1–1350012 .
  • Bourbaki , N. ( 1985 ). Algèbre Commutative . Chapitres 5 à 7 . Paris : Masson .
  • Fedder , R. , Huneke , C. , Hübl , R. ( 1990 ). Zeros of differentials along one-fibered ideals . Proc. Amer. Math. Soc. 108 ( 2 ): 319 – 325 .
  • Hübl , R. , Swanson , I. ( 2001 ). Discrete valuations centered on local domains . Journal of Pure and Applied Algebra 161 ( 1–2 ): 145 – 166 .
  • Katz , D. (1986). On the number of minimal prime ideals in the completion of a local ring. Rocky Mountain J. Math. 16:575–578.
  • Katz , D. , Validashti , J. ( 2010 ). Multiplicities and Rees valuations . Collectanea Mathematica 61 ( 1 ): 1 – 24 .
  • Matsumura , H. ( 1970 ). Commutative Algebra . New York : Benjamin .
  • Matsumura , H. ( 1986 ). Commutative Ring Theory . Cambridge Studies in Advanced Mathematics, Vol. 8. New York : Cambridge University Press .
  • Nagata , M. ( 1962 ). Local Rings. Interscience Tracts in Pure and Applied Mathematics . New York-London : John Wiley & Sons .
  • Rees , D. ( 1961 ). A note on analytically unramified local rings. J. London Math. Soc. 24–28 .
  • Rees , D. ( 1989 ). Izumi's theorem . In: Hochster , M. , Huneke , C. , Sally , J. D. , eds. Commutative Algebra . Springer-Verlag , pp. 407 – 416 .
  • Sally , J. ( 1989 ). One-fibered ideals . In: Commutative Algebra (Berkeley, CA, 1987). Math. Sci. Res. Inst. Publ., 15 . New York : Springer-Verlag , pp. 437 – 442 .
  • Swanson , I. ( 2011 ). Rees valuations . In: Fontana , M. , Kabbaj , S.-E. , Olberding , B. , Swanson , I. , eds. Commutative algebra, Noetherian and non-Noetherian perspectives . Vol. VIII. New York : Springer , pp. 421 – 440 .
  • Swanson , I. , Huneke , C. ( 2006 ). Integral Closure of Ideals, Rings, and Modules. London Math. Soc. Lecture note Series 336 .
  • 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.