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On the proof of a fundamental theorem in the theory of algebras. (Beweis eines Hauptsatzes in der Theorie der Algebren.) (German) Zbl 0003.24404
The authors have answered an important outstanding question by proving that every normal division algebra over an algebraic field is a cyclic (Dickson) algebra. Hasse has applied this theorem (I) to show that the exponent of a normal simple algebra over an algebraic field is equal to its index, (2) to obtain extensions of theorems on class fields to general relative Galois fields, and (3) to prove that the absolutely irreducible representations of a finite group are all possible in cyclotomic fields.

MSC:
12E15 Skew fields, division rings
11R52 Quaternion and other division algebras: arithmetic, zeta functions
16K20 Finite-dimensional division rings
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