Cyclic Division Algebras

  • Richard S. Pierce
Part of the Graduate Texts in Mathematics book series (GTM, volume 88)


The first examples of division algebras that were found after the quaternions belong to the class of cyclic division algebras. This class still plays a major role in the theory of central simple algebras. If is a local field, an algebraic number field, or more generally a global field, then every central division algebra over F is cyclic. This fact will be proved later; it is one of the most profound results in this book.


Division Algebra Galois Extension Quaternion Algebra Primary Decomposition Fixed Field 


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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Richard S. Pierce
    • 1
  1. 1.University of ArizonaTucsonUSA

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