Dihedral algebras are cyclic
Pascal Mammone, Jean-Pierre Tignol · Proceedings of the American Mathematical Society · 1987
This note gives a simple proof of the following theorem of Rowen and Saltman: Every central simple algebra split by a Galois extension of rank 2 n 2n ( n n odd) with dihedral Galois group is cyclic if the center contains a primitive n n th root of unity .