Division Algebras over Number Fields
In this chapter we come to some of the deepest and most beautiful results in modern algebra. These are the theorems that classify and describe the central simple algebras over algebraic number fields. This work is associated with the names of several of the greatest heroes of mathematics: Hasse, Brauer, Noether, and Albert. It is based on developments in number theory that are due to Kronecker, Weber, Hilbert, Minkowski, Furtwangler, Artin, Takagi, Hasse, Witt, and many others.
KeywordsPrime Divisor Division Algebra Algebraic Number Galois Extension Basic Theorem
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