On the stabilization of the general linear group over a ring

We are concerned with the theory of matrix determinants (more precisely, the Whitehead determinant) over any associative ring from the algebraic point of view, i.e. $K_1$-theory. The main goal of the paper is to prove the results on the “stabilization” of the general linear group over a ring, which were announced by the author in the journal “Functional analysis”, vol. 3, № 2 (1969). In passing we reproduce all the results of H. Bass and the author relating to this.
Bibliography: 9 titles.