Summary: Journal of Pure and Applied Algebra 182 (2003) 109117
Projective Schur groups of iterated power series
Eli Aljade , Jack Sonn
Department of Mathematics, Technion-Israel Institute of Technology, Haifa 3200, Israel
Received 11 March 2002; accepted 24 October 2002
Communicated by A.V. Geramita
The BrauerWitt Theorem states that every Schur algebra over a ˙eld K is Brauer equivalent
to a cyclotomic algebra. A central conjecture on the projective Schur group of a ˙eld is the
analogue of this theorem, which asserts that every projective Schur algebra over a ˙eld K is
Brauer equivalent to a radical algebra. The conjecture is so far known to be true in characteristic
p and for local and global ˙elds. The next natural class of ˙elds to test is power series ˙elds
over local and global ˙elds. In this paper we verify the conjecture for these ˙elds and more
generally for iterated power series ˙elds over local and global ˙elds.
c 2003 Elsevier Science B.V. All rights reserved.
MSC: 11R52; 11S25; 12F05; 12G05; 13A20
Let K be a ˙eld, Br(K) its Brauer group. The projective Schur group PS(K) of