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A generalization of Brauer's theorem on splitting fields to semigroups

✍ Scribed by Janez Bernik

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
84 KB
Volume
266
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let F be either an algebraic number field or a p-adic field and A a central simple algebra over F . Suppose A is spanned by a multiplicative semigroup Ξ“ βŠ‚ A with the property that the minimal polynomial of every g ∈ Ξ“ splits over F . Then A represents the trivial class in the Brauer group of F .

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