Vaserstein, L. N. On the stabilization of the general linear group over a ring. (English. Russian original) Zbl 0238.20057 Math. USSR, Sb. 8(1969), 383-400 (1970); translation from Mat. Sb., n. Ser. 79(121), 405-424 (1969). Summary: 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 [Funct. Anal. Appl. 3, 152–154 (1969); translation from Funkts. Anal. Prilozh. 3, No. 2, 85–86 (1969; Zbl 0208.04401)]. In passing we reproduce all the results of H. Bass and the author relating to this. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 59 Documents MSC: 20G35 Linear algebraic groups over adèles and other rings and schemes 16E20 Grothendieck groups, \(K\)-theory, etc. 19B14 Stability for linear groups 19B10 Stable range conditions 19B28 \(K_1\) of group rings and orders Keywords:Whitehead determinant; \(K_1\)-theory; stabilization of the general linear group Citations:Zbl 0208.04401 PDFBibTeX XMLCite \textit{L. N. Vaserstein}, Math. USSR, Sb. 8, 383--400 (1970; Zbl 0238.20057); translation from Mat. Sb., n. Ser. 79(121), 405--424 (1969) Full Text: DOI MNR