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Division algebras of prime degree with infinite genus
The genus gen(D) of a finite-dimensional central division algebra D over a
field F is defined as the collection of classes [D'] in the Brauer group Br(F),
where D' is a central division F-algebra having the same maximal subfields as
D. For any prime p, we construct a division algebra of degree p with infinite
genus. Moreover, we show that there exists a field K such that there are
infinitely many nonisomorphic central division K-algebras of degree p, and any
two such algebras have the same genus.Comment: 4 page
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