ON THE STABILIZATION OF THE GENERAL LINEAR GROUP OVER A RING

Abstract

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. K1-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, no. 2 (1969). In passing we reproduce all the results of H. Bass and the author relating to this. The bibliography contains 9 items.