Progress on the dimension question for power series rings

  • Jim Coykendall


Power Series Prime Ideal Valuation Domain Countable Collection Power Series Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Al]
    J. Arnold.: Krull dimension in power series rings. Trans. Amer. Math. Soc. 177, 299–304 (1973)CrossRefMathSciNetzbMATHGoogle Scholar
  2. [A2]
    J. Arnold.: Power series rings over discrete valuation rings. Pacific J. Math. 93, 31–33 (1981)MathSciNetzbMATHGoogle Scholar
  3. [A3]
    J. Arnold.: Power series rings with finite Krull dimension. Indiana Univ. Math. J. 31, 897–911 (1982)CrossRefMathSciNetzbMATHGoogle Scholar
  4. [AB]
    J. Arnold and J. Brewer.: When (D[[X]])P[[X]] is a valuation ring. Proc. Amer. Math. Soc. 37, 326–332 (1973)CrossRefMathSciNetzbMATHGoogle Scholar
  5. [B.
    J. Brewer.: Power series over commutative rings. Dekker, (1981)Google Scholar
  6. [CC]
    J. Condo, J. Coykendall.: Strong convergence properties of SET rings. Comm. Algebra 27, 2073–2085 (1999)MathSciNetzbMATHGoogle Scholar
  7. [CCD]
    J. Condo, J Coykendall, D. Dobbs.: Formal power series rings over zerodimensional SFT-rings. Comm. Algebra 24, 2687–2698 (1996)MathSciNetzbMATHGoogle Scholar
  8. [C]
    J. Coykendall.: The SFT property does not imply finite dimension for power series rings. J. Algebra 256, 85–96 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  9. [CD]
    J. Coykendall, D. Dobbs.: Fragmented domains have infinite KruU dimension. Rend. Circ. Mat. Palermo 50, 377–388 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. [F]
    D. Fields.: Dimension theory in power series rings. Pacific J. Math. 35, 326–332 (1970)MathSciNetGoogle Scholar
  11. [G]
    R. Gilmer.: Dimension theory of power series rings over a commutative ring. Algebra and logic (Fourteenth Summer Res. Inst., Austral. Math. Soc, Monash Univ., Clayton, 1974), Lecture Notes in Math., Vol. 450. Springer, Berlin Heidelberg New York, 155–162 (1975)Google Scholar
  12. [KPl]
    B. Kang and M. Park. A localization of a power series ring over a valuation domain. J. Pure Appl. Algebra 140, 107–124 (1999)CrossRefMathSciNetzbMATHGoogle Scholar
  13. [KP2]
    B. Kang and M. Park. Krull dimension in power series rings. Preprint.Google Scholar
  14. [K]
    I. Kaplansky. Commutative Rings. University of Chicago Press, Chicago (1974)zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  • Jim Coykendall
    • 1
  1. 1.Department of MathematicsNorth Dakota State UniversityFargo

Personalised recommendations