Mathematische Zeitschrift

, Volume 190, Issue 2, pp 151–162 | Cite as

Sums of squares in division algebras

  • David B. Leep
  • Daniel B. Shapiro
  • Adrian R. Wadsworth
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A1]
    Albert, A.A.: A construction of noncyclic normal division algebras. Bull. Amer. Math. Soc.38, 449–456 (1932)Google Scholar
  2. [A2]
    Albert, A.A.: Structure of algebras. Amer. Math. Soc. Colloq. Publ., Vol.24, 1939; revised 1961Google Scholar
  3. [A3]
    Albert, A.A.: On ordered algebras. Bull. Amer. Math. Soc.46, 521–522 (1940)Google Scholar
  4. [A4]
    Albert, A.A.: Modern higher algebra. University of Chicago Press 1958Google Scholar
  5. [Am1]
    Amitsur, S.A.: Invariant submodules of simple rings. Proc. Amer. Math. Soc.7, 987–989 (1956)Google Scholar
  6. [Am2]
    Amitsur, S.A.: On central division algebras. Israel J. Math.12, 408–420 (1972)Google Scholar
  7. [Ar]
    Artin, E.: Geometric algebra. New York: Interscience 1957Google Scholar
  8. [As]
    Asano, S.: On invariant subspaces of division algebras. Kōdai Math. Sem. Rep.18, 322–334 (1966)Google Scholar
  9. [DD]
    Diller, J., Dress, A.: Zur Galoistheorie pythagoreischer Körper. Arch. Math.16, 148–152 (1965)Google Scholar
  10. [ELP]
    Elman, R., Lam, T.Y., Prestel, A.: On some Hasse principles over formally real fields. Math. Z.134, 291–301 (1973)Google Scholar
  11. [G]
    Garver, R.: Quartic equations with certain groups. Ann. Math.29, 47–51 (1928)Google Scholar
  12. [GK]
    Griffin, M., Krusemeyer, M.: Matrices as sums of squares. Linear Multinear Algebra5, 33–44 (1977)Google Scholar
  13. [H1]
    Herstein, I.N.: Noncommutative rings. Carus Monograph 15. Math. Assoc. Amer. 1968Google Scholar
  14. [H2]
    Herstein, I.N.: Topics in ring theory. Univ. of Chicago Press 1969Google Scholar
  15. [J]
    Jacobson, N.: PI-Algebras. An introduction Lecture Notes in Math. Vol. 441. Berlin-Heidelberg-New York: Springer 1975Google Scholar
  16. [K]
    Kasch, F.: Invariante Untermoduln des Endomorphismenringes eines Vektorraums. Arch. Math.4, 182–190 (1953)Google Scholar
  17. [L1]
    Lam, T.Y.: The algebraic theory of quadratic forms. Reading, Mass.: Benjamin 1973Google Scholar
  18. [L2]
    Lam, T.Y.: Orderings, valuations and quadratic forms. CBMS Notes, No.52, Amer. Math. Soc. 1983Google Scholar
  19. [P]
    Pierce, R.S.: Associative algebras. Berlin-Heidelberg-New York: Springer 1982Google Scholar
  20. [Pr1]
    Prestel, A.: Quadratische Semiordnungen und quadratische Formen. Math. Z.133, 319–342 (1973)Google Scholar
  21. [Pr2]
    Prestel, A.: Lectures on formally real fields. IMPA Lecture Notes. Rio de Janeiro 1975Google Scholar
  22. [R]
    Reiner, I.: Maximal orders. New York-London: Academic Press 1975Google Scholar
  23. [Ros]
    Rosenberg, A.: The Cartan-Brauer-Hua theorem for matrix and local matrix rings. Proc. Amer. Math. Soc.7, 891–898 (1956)Google Scholar
  24. [Ro]
    Rowen, L.H.: Polynomial identities in ring theory. New York-London: Academic Press 1980Google Scholar
  25. [Sz]
    Szele, T.: On ordered skew fields. Proc. Amer. Math. Soc.3, 410–413 (1952)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • David B. Leep
    • 1
  • Daniel B. Shapiro
    • 2
  • Adrian R. Wadsworth
    • 3
  1. 1.University of California at BerkeleyBerkeleyUSA
  2. 2.The Ohio State UniversityColumbusUSA
  3. 3.University of California at San DiegoLa JollaUSA

Personalised recommendations