 
Summary: ISRAEL JOURNAL OF MATHEMATICS 131 (2002), 375379
FIELDS FOR WHICH THE PROJECTIVE SCHUR
SUBGROUP IS THE WHOLE BRAUER GROUP
BY
ELI ALJADEFF AND JACK SONN
Department of Mathematics, Technion  Israel Institute of Technology
Haifa 32000, Israel
email: aljadeff@math.technion.ac.il, sonn@math.technion.ac.il
ABSTRACT
Let Br(K) denote the Brauer group of a field K and PS(K) the
projective Sehur subgroup.
i. Let K be a finitely generated infinite field. Then PS(K) =Br(K)
if and only if I( is a global field.
2. Let /x~ be a finitely generated infinite field, and let K((t)) denote
the field of formal power series in t over /iv. Then P S ( K ( ( t ) ) ) 
Br(K((t))) if and only if K = Q.
1. Introduction
Let K be any field. The projective Schur (sub)group PS(K) of a field K is
the subgroup of the Brauer group Br(K) generated by (in fact, consisting of) all
classes that are represented by a projective Schur algebra A. A finite dimensional
