All dihedral division algebras of degree five are cyclic

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In 1982 Rowen and Saltman proved that every division algebra which is split by a dihedral extension of degree 2n of the center, n odd, is in fact cyclic. The proof requires roots of unity of order n in the center. We show that for n = 5, this assumption can be removed. It then follows that 5Br(F), the 5-torsion part of the Brauer group, is generated by cyclic algebras, generalizing a result of Merkurjev (1983) on the 2 and 3 torsion parts.

Original languageEnglish
Pages (from-to)1925-1931
Number of pages7
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - Jun 2008


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