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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 844–873 (Mi izv2061)  

This article is cited in 7 scientific papers (total in 7 papers)

Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity

I. A. Volodin


Abstract: Algebraic $K$-theory can be constructed by means of the homotopy groups of the abstract simplicial structure on the group of invertible matrices $GL(A)$ of the ring $A$. This structure may be naturally taken as two-sidedly invariant. Of basic interest is the multiplication in the functor so obtained, which for different rings $A$ assumes different aspects.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 859–887

Bibliographic databases:

UDC: 513.836
MSC: Primary 18F25; Secondary 16A54
Received: 27.07.1970

Citation: I. A. Volodin, “Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 844–873; Math. USSR-Izv., 5:4 (1971), 859–887

Citation in format AMSBIB
\Bibitem{Vol71}
\by I.~A.~Volodin
\paper Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 4
\pages 844--873
\mathnet{http://mi.mathnet.ru/izv2061}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=296140}
\zmath{https://zbmath.org/?q=an:0229.18010}
\transl
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 4
\pages 859--887
\crossref{https://doi.org/10.1070/IM1971v005n04ABEH001121}


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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. Vasershtein, “Osnovy algebraicheskoi $K$-teorii”, UMN, 28:2(170) (1973), 231–232  mathnet  zmath
    2. Kh. N. Inasaridze, “Homotopy of pseudosimplicial groups, nonabelian derived functors, and algebraic $K$-theory”, Math. USSR-Sb., 27:3 (1975), 303–324  mathnet  crossref  mathscinet  zmath
    3. A. S. Mishchenko, “Hermitian $K$-theory. The theory of characteristic classes and methods of functional analysis”, Russian Math. Surveys, 31:2 (1976), 71–138  mathnet  crossref  mathscinet  zmath
    4. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    5. J.B. Wagoner, “Equivalence of algebraic K-theories”, Journal of Pure and Applied Algebra, 11:1-3 (1977), 245  crossref
    6. V. M. Dergachev, “Algebraic $K$-groups as homotopy groups of a simplicial analogue of Grassmann manifolds”, Russian Math. Surveys, 45:5 (1990), 227–228  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. Marc Levine, “Relative MilnorK-theory”, K-Theory, 6:2 (1992), 113  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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