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, No 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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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/

[1] H. Bass, “$K$-theory and stable algebra”, Publ. Math., 22 (1964), 5–60 | MR | Zbl

[2] H. Bass, J. Milnor, J.-P. Serre, “Solution cf the congruence subgroup problem for $SL_n$ ($n\geqslant3$) and $SP_{2n}$ ($n\geqslant2$)”, Publ. Math., 33 (1967), 59–137 | MR | Zbl

[3] L. N. Vasershtein, “$K_1$-teoriya i kongruentsproblema”, Matem. zametki, 5:2 (1969), 233–244

[4] J. Dieudonne, “Les determinants sur un corps non commutatif”, Bull. Soc. Math. France, 71 (1943), 27–45 | MR | Zbl

[5] W. Klingenberg, “Die Structur der linearen Gruppe über einen nichtkommutativen lokalen Ring”, Arch. Math., 13 (1962), 73–81 | DOI | MR | Zbl

[6] P. M. Cohn, “On the structure of the $GL_2$ of a ring”, Publ. Math., 30 (1966), 365–413 | MR | Zbl

[7] H. Bass, Lectures on topics in algebraic $K$-theory, Bombay, 1967

[8] L. N. Vasershtein, “O stabilizatsii v algebraicheskoi $K$-teorii”, Funkts. analiz, 3:2 (1909), 85–86 | MR

[9] Dzh. Milnor, “Kruchenie Uaitkheda”, Matematika, 11:1 (1967), 3–42 | MR