Given two central simple algebras "A" ~ "M"("n","S") and "B" ~ "M"("m","T") over the same field "F", "A" and "B" are called "similar" (or "Brauer equivalent") if their division rings "S" and "T" are isomorphic. The set of all equivalence classes of central simple algebras over a given field "F", under this equivalence relation, can be equipped with a group operation given by the tensor product of algebras. The resulting group is called the Brauer group Br("F") of the field "F". It is always a torsion group.