In this paper we discuss the Brauer group of a field and its connections with cohomology groups. Definitions involving central simple algebras lead to a discussion of splitting fields, which are the important step in the connection of the Brauer group with cohomology groups. Finally, once the connection between the Brauer group and cohomology groups is established, the paper finishes by calculating specific examples of cocycles associated to certain classes of central simple algebras.
Justin Sawon, Associate Professor and Director of Graduate Studies, Department of Mathematics, University of North Carolina - Chapel Hill
"The Brauer Group of a Field,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 18
, Article 6.
Available at: https://scholar.rose-hulman.edu/rhumj/vol18/iss2/6