ABSTRACT
Brauer group of a field will serve as the target group for important invariants of quadratic forms. Introducing Brauer group we try to keep the conceptual machinery at a minimum. We can afford that since we are not going to study Brauer groups for themselves but use them only in their limited role of the home of Hasse and Witt invariants. The usual context for Brauer groups is the famous Wedderburn’s theorem on the structure of simple algebras. We will not use the more involved existence part of Wedderburn’s theorem but we cannot do without the uniqueness part. Thus we prove only the latter using the classical approach via clever matrix calculations discovered by the old masters.
