States Dieudonne Determinant Computation of K_1 of a Division Ring: Let D be a division ring. For n 1, let GL_n(D) be the group of invertible n n matrices over D, let GL(D)= _n GL_n(D) under the stabilization maps A diag(A,1), and let E(D) GL(D) be the stable elementary subgroup generated by all elementary transvections e_ij(r)=I_n+rE_ij with n 2, 1 i j n, and r D, where I_n is the identity matrix and E_ij is the matrix unit.