Cyclic Division Algebras
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.
KeywordsDivision Algebra Galois Extension Quaternion Algebra Primary Decomposition Fixed Field
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