Let Br(K) denote the Brauer group of a field K and PS(K) the projective Schur subgroup. 1. Let K be a finitely generated infinite field. Then PS(K) = Br(K) if and only if K is a global field. 2. Let K be a finitely generated infinite field, and let K((t)) denote the field of formal power series t over K. Then PS(K((t))) = Br(K((t))) if and only if K = ℚ.