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Mat. Zametki, 1969, Volume 5, Issue 2, Pages 233–244 (Mi mz6828)  

This article is cited in 11 scientific papers (total in 11 papers)

$K_1$-theory and the congruence problem

L. N. Vaserstein


Abstract: The following results are presented: a) A $K_1$-functor of a noncommutative ring with unity is a factor of a general linear group with respect to the subgroup of elementary matrices; b) a description is given of all the subgroups of finite index in a special linear group over the order in a field.

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English version:
Mathematical Notes, 1969, 5:2, 141–148

Bibliographic databases:

UDC: 513.83
Received: 23.12.1967

Citation: L. N. Vaserstein, “$K_1$-theory and the congruence problem”, Mat. Zametki, 5:2 (1969), 233–244; Math. Notes, 5:2 (1969), 141–148

Citation in format AMSBIB
\Bibitem{Vas69}
\by L.~N.~Vaserstein
\paper $K_1$-theory and the congruence problem
\jour Mat. Zametki
\yr 1969
\vol 5
\issue 2
\pages 233--244
\mathnet{http://mi.mathnet.ru/mz6828}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=246941}
\zmath{https://zbmath.org/?q=an:0195.32202}
\transl
\jour Math. Notes
\yr 1969
\vol 5
\issue 2
\pages 141--148
\crossref{https://doi.org/10.1007/BF01098314}


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  • http://mi.mathnet.ru/eng/mz/v5/i2/p233

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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, “On the stabilization of the general linear group over a ring”, Math. USSR-Sb., 8:3 (1969), 383–400  mathnet  crossref  mathscinet  zmath
    2. 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
    3. L. N. Vaserstein, “Stable rank of rings and dimensionality of topological spaces”, Funct. Anal. Appl., 5:2 (1971), 102–110  mathnet  crossref  mathscinet  zmath
    4. L. N. Vaserstein, “On the group $SL_2$ over Dedekind rings of arithmetic type”, Math. USSR-Sb., 18:2 (1972), 321–332  mathnet  crossref  mathscinet  zmath
    5. 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
    6. L. N. Vaserstein, “Stabilization for classical groups over rings”, Math. USSR-Sb., 22:2 (1974), 271–303  mathnet  crossref  mathscinet  zmath
    7. L. N. Vasershtein, “O stabilizatsii dlya $K_2$-funktora Milnora”, UMN, 30:1(181) (1975), 224–224  mathnet  mathscinet  zmath
    8. L. N. Vaserstein, A. A. Suslin, “Serre's problem on projective modules over polynomial rings, and algebraic $K$-theory”, Math. USSR-Izv., 10:5 (1976), 937–1001  mathnet  crossref  mathscinet  zmath
    9. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    10. 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
    11. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
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