Brauer factor sets and simple algebras

Author:
Louis H. Rowen

Journal:
Trans. Amer. Math. Soc. **282** (1984), 765-772

MSC:
Primary 16A39; Secondary 12E15, 16A38

DOI:
https://doi.org/10.1090/S0002-9947-1984-0732118-3

MathSciNet review:
732118

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Abstract: It is shown that the Brauer factor set of a finite-dimensional division algebra of odd degree can be chosen such that for all and . This implies at once the existence of an element with ; the coefficients of and in the characteristic polynomial of are thus 0. Also one gets a generic division algebra of degree whose center has transcendence degree , as well as a new (simpler) algebra of generic matrices. Equations are given to determine the cyclicity of these algebras, but they may not be tractable.

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DOI:
https://doi.org/10.1090/S0002-9947-1984-0732118-3

Article copyright:
© Copyright 1984
American Mathematical Society