72
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Rank One Discrete Valuations of Power Series Fields

, &
Pages 2533-2551 | Received 30 Nov 2005, Published online: 14 Aug 2007

REFERENCES

  • Abhyankar , S. ( 1956 ). On the valuations centered in a local domain . Amer. J. Math. 78 : 321 – 348 .
  • Briales , E. ( 1989 ). Constructive theory of valuations . Comm. Algebra 17 : 1161 – 1177 .
  • Briales , E. , Herrera , F. J. ( 1985 ). Construcción Explícita de las Valoraciones de un Anillo de Series Formales en dos Variables . Actas X Jornadas Hispano-Lusas , Murcia , vol. II , pp. 1 – 10 .
  • Herrera , J. , Olalla , M. A. , Spivakovsky , M. , Teissier , B. ( 2003 ). Implicit ideals of a valuation centered in a local domain . Prepublicación no. 23 del Departamento de Álgebra de la Universidad de Sevilla .
  • Kaplansky , I. ( 1942 ). Maximal fields with valuations I . Duke Math. Journ. 9 : 303 – 321 .
  • Krull , W. ( 1932 ). Allgemeine Bewerstungstheorie . J. Reine Angew. Math. 167 : 160 – 196 .
  • Olalla , M. A. ( 2001 ). On the dimension of discrete valuations of k((X 1,…, X n )) . C. R. Acad. Sci. Paris, Sér Math. 333 : 27 – 32 .
  • Serre , J. P. ( 1962 ). Corps Locaux . Publications de l'Institut de Mathmatique de l'Universit de Nancago, VIII Actualits Sci. Indust., No. 1296 . Paris : Hermann .
  • Spivakovsky , M. ( 1996 ). Resolution of singularities I: Local uniformization . Preprint . University of Toronto .
  • Teissier , B. ( 2003 ). Valuations, Deformations, and Toric Geometry . Valuation theory and its applications, Saskatoon, Canada, 1999, Vol. II:361–459. Fields Inst. Commun., 33 . Providence, RI: Amer. Math. Soc.
  • Zariski , O. , Samuel , P. ( 1975 ) Commutative Algebra . Graduate Texts in Mathematics, Vol. II . New York-Heidelberg-Berlin: Springer-Verlag .
  • Communicated by A. Elduque.

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.