TY - JOUR

T1 - All dihedral division algebras of degree five are cyclic

AU - Matzri, Eliyahu

PY - 2008/6

Y1 - 2008/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950648843&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09310-6

DO - 10.1090/S0002-9939-08-09310-6

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SN - 0002-9939

VL - 136

SP - 1925

EP - 1931

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 6

ER -