Splitting of algebras by function fields of one variable

LetKbe a field and(K) the Brauer group ofK. It consists of the similarity classes of finite central simple algebras overK. For any field extensionF/Kthere is a natural mapping(K) →(F) which is obtained by assigning to each central simple algebraA/Kthe tensor productwhich is a central simple algebra overF. The kernel of this map is the relative Brauer group(F/K), consisting of thoseA ∈(K) which are split byF.