Journal of Mathematical Sciences

, Volume 140, Issue 2, pp 333–339 | Cite as

Hölder rigidity for matrices

  • M. H. Hosseini


It is proved that a (C 1, C 2)-Hölder valuation is (2, α)-equivalent to classical valuation on the set of matrices over a skew field and on the set of cubic matrices over a field. These results provide an extension of the Garcia theorem.


Division Ring Detailed Exposition Space Matrix General Division Indian Math 
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.


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  1. 1.
    P. M. Cohn, “The construction of valuations on skew fields,” J. Indian Math. Soc., 54, 1–45 (1989).MathSciNetGoogle Scholar
  2. 2.
    P. M. Cohn, Skew Fields, Theory of General Division Rings, Cambridge University Press, Cambridge (1995).MATHGoogle Scholar
  3. 3.
    M. Lecat, “Coup d’oeil sur la theorie des determinants superieurs dans son état actuel,” Ann. Soc. Sci. Bruxelles, 45, II, fasc. 1/2, 1–98 (1926); fasc. 3/4, 141–168; 46, 15–54 (1926); 47, serie A, II, fasc. 1, 1–37 (1927).Google Scholar
  4. 4.
    M. Mahdavi-Hezavehi, “Matrix valuations and their associated skew fields,” Resultate d. Math., 5, 149–156 (1982).MathSciNetGoogle Scholar
  5. 5.
    E. Munoz Garcia, “Hölder absolute values are equivalent to classical ones,” Proc. Amer. Math. Soc., 127, No. 7, 1967–1971 (1999).CrossRefMathSciNetGoogle Scholar
  6. 6.
    L. H. Rice, “Introduction to higher determinants,” J. Math. Phys., 9, 47–71 (1930).Google Scholar
  7. 7.
    N. P. Sokolov, Space Matrices and Their Applications [in Russian], Fizmatlit, Moscow (1960).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • M. H. Hosseini
    • 1
  1. 1.University of BirdjandIran

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