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Mat. Sb. (N.S.), 1969, Volume 79(121), Number 3(7), Pages 405–424 (Mi msb3595)  

This article is cited in 55 scientific papers (total in 55 papers)

On the stabilization of the general linear group over a ring

L. N. Vaserstein

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. $K_1$-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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English version:
Mathematics of the USSR-Sbornik, 1969, 8:3, 383–400

Bibliographic databases:

UDC: 512.864
MSC: 19B14, 19B10, 19B28, 15A15, 16S50
Received: 12.12.1968

Citation: L. N. Vaserstein, “On the stabilization of the general linear group over a ring”, Mat. Sb. (N.S.), 79(121):3(7) (1969), 405–424; Math. USSR-Sb., 8:3 (1969), 383–400

Citation in format AMSBIB
\by L.~N.~Vaserstein
\paper On~the stabilization of the general linear group over a~ring
\jour Mat. Sb. (N.S.)
\yr 1969
\vol 79(121)
\issue 3(7)
\pages 405--424
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 3
\pages 383--400

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    This publication is cited in the following articles:
    1. L. N. Vaserstein, “Stabilization of unitary and orthogonal groups over a ring with involution”, Math. USSR-Sb., 10:3 (1970), 307–326  mathnet  crossref  mathscinet  zmath
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    3. L. N. Vaserstein, “The structure of classical arithmetic groups of rank greater than one”, Math. USSR-Sb., 20:3 (1973), 465–492  mathnet  crossref  mathscinet  zmath
    4. I. Z. Golubchik, “O polnoi lineinoi gruppe nad assotsiativnym koltsom”, UMN, 28:3(171) (1973), 179–180  mathnet  mathscinet  zmath
    5. L. N. Vaserstein, “Stabilization for classical groups over rings”, Math. USSR-Sb., 22:2 (1974), 271–303  mathnet  crossref  mathscinet  zmath
    6. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    7. A. A. Suslin, “On the structure of the special linear group over polynomial rings”, Math. USSR-Izv., 11:2 (1977), 221–238  mathnet  crossref  mathscinet  zmath
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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