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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.

Full text: PDF file (1844 kB)
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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
\Bibitem{Vas69}
\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
\mathnet{http://mi.mathnet.ru/msb3595}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=267009}
\zmath{https://zbmath.org/?q=an:0238.20057}
\transl
\jour Math. USSR-Sb.
\yr 1969
\vol 8
\issue 3
\pages 383--400
\crossref{https://doi.org/10.1070/SM1969v008n03ABEH001279}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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
    2. L. N. Vaserstein, “Stable rank of rings and dimensionality of topological spaces”, Funct. Anal. Appl., 5:2 (1971), 102–110  mathnet  crossref  mathscinet  zmath
    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
    8. A. A. Suslin, “On stably free modules”, Math. USSR-Sb., 31:4 (1977), 479–491  mathnet  crossref  mathscinet  zmath  isi
    9. Susan C. Geller, “On some new algebraic K-groups”, Journal of Pure and Applied Algebra, 11:1-3 (1977), 157  crossref
    10. A. A. Suslin, “Reciprocity laws and the stable rank of polynomial rings”, Math. USSR-Izv., 15:3 (1980), 589–623  mathnet  crossref  mathscinet  zmath  isi
    11. Sushil Jajodia, Bruce A. Magurn, “Surjective stability of units and simple homotopy type”, Journal of Pure and Applied Algebra, 18:1 (1980), 45  crossref
    12. M. S. Tulenbaev, “The Steinberg group of a polynomial ring”, Math. USSR-Sb., 45:1 (1983), 139–154  mathnet  crossref  mathscinet  zmath
    13. Suslin A., “Mennicke Symbols and their Applications in the K-Theory of Fields”, 966, 1982, 334–356  isi
    14. Ravi Rao, “Stability theorems for overrings of polynomial rings, II”, Journal of Algebra, 78:2 (1982), 437  crossref
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    22. Vaserstein L., “Computation of K1 via Mennicke Symbols”, Commun. Algebr., 15:3 (1987), 611–656  crossref  isi
    23. Daniel Guin, “Homologie du groupe linéaire et K-théorie de Milnor des anneaux”, Journal of Algebra, 123:1 (1989), 27  crossref
    24. Wilberd Van Der Kallen, “A module structure on certain orbit sets of unimodular rows”, Journal of Pure and Applied Algebra, 57:3 (1989), 281  crossref
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    26. A. W. Mason, “Subnormal subgroups of En( R) have no free, non-abelian quotients, when n≧3”, Proc Edin Math Soc, 34:1 (1991), 113  crossref  mathscinet  zmath
    27. Joseph Gubeladze, “The elementary action on unimodular rows over a monoid ring”, Journal of Algebra, 148:1 (1992), 135  crossref
    28. A.J. Berrick, Derek J.S. Robinson, “Imperfect groups”, Journal of Pure and Applied Algebra, 88:1-3 (1993), 3  crossref
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    30. Nikolai Vavilov, Eugene Plotkin, “Chevalley groups over commutative rings: I. Elementary calculations”, Acta Appl Math, 45:1 (1996), 73  crossref  mathscinet  zmath  isi  elib
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  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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