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    Berhuy, G. Grenier-Boley, N. and Mahmoudi, M. G. 2013. Sums of values represented by a quadratic form. Manuscripta Mathematica, Vol. 140, Issue. 3-4, p. 531.


    Hoffmann, Detlev W. 2011. LEVELS AND SUBLEVELS OF QUATERNION ALGEBRAS. Mathematical Proceedings of the Royal Irish Academy, Vol. 110, Issue. -1, p. 95.


    O'Shea, James 2011. BOUNDS ON THE LEVELS OF COMPOSITION ALGEBRAS. Mathematical Proceedings of the Royal Irish Academy, Vol. 110, Issue. -1, p. 21.


    O'Shea, James 2007. Levels and sublevels of composition algebras. Indagationes Mathematicae, Vol. 18, Issue. 1, p. 147.


    Laghribi, Ahmed and Mammone, Pasquale 2001. ON THE LEVEL OF A QUATERNION ALGEBRA. Communications in Algebra, Vol. 29, Issue. 4, p. 1821.


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Levels of division algebras

  • David B. Leep (a1)
  • DOI: http://dx.doi.org/10.1017/S0017089500009447
  • Published online: 01 May 2009
Abstract

In [7] the level, sublevel, and product level of finite dimensional central division algebras D over a field F were calculated when F is a local or global field. In Theorem 1.4 of this paper we calculate the same quantities if all finite extensions K of F satisfy ū(K) ≤2, where ū is the Hasse number of a field as defined in [2]. This occurs, for example, if F is an algebraic extension of the function field R(x) where R is a real closed field or hereditarily Euclidean field (see [4]).

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3.R. Elman and T. Y. Lam , Quadratic forms over formally real fields and Pythagorean fields, Amer. J. Math. 94 (1972), 11551194.

4.R. Elman , T. Y. Lam and A. Prestel , On some Hasse principles over formally real fields, Math. Z. 134 (1973), 291301.

7.D. B. Leep , J.-P. Tignol and N. Vast , The level of division algebras over local and global fields. J. Number. Theory 33 (1989), 5370.

8.D. B. Leep and A. R. Wadsworth , The transfer ideal of quadratic forms and a Hasse norm theorem mod squares, Trans. Amer. Math. Soc. 315 (1989), 415431.

9.D. W. Lewis , Levels of quaternion algebras, Rocky Mountain J. Math., 19 (1989), 787792.

11.W. Scharlau , Quadratic forms and hermitian forms (Springer, 1985).

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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