Geodesic
On~the stabilization of the general linear group over a~ring
Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 383-400

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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. 
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     author = {L. N. Vaserstein},
     title = {On~the stabilization of the general linear group over a~ring},
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L. N. Vaserstein. On~the stabilization of the general linear group over a~ring. Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 383-400. http://geodesic.mathdoc.fr/item/SM_1969_8_3_a4/