(?/2?)~4-crossed products of exponent 2

摘要

Let k be a field of characteristic distinct from 2, a, a_1, a_2, a_3 ε k*, D ε _2 Br k, exp D = 2, D_k (√a, √a_1}, √a_2}, √a_3})} = 0. We prove that D is a sum of 18 quaternion algebras. Also for a field F of certain type we construct a certain function f(ind D) such that D is a sum of f(ind D) quaternions for any D ε _2 Br (F).