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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.

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

Citations:

Zbl 0208.04401
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