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

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

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
2. Kh. N. Inasaridze, “Homotopy of pseudosimplicial groups, nonabelian derived functors, and algebraic $K$-theory”, Math. USSR-Sb., 27:3 (1975), 303–324
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
4. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156
5. J.B. Wagoner, “Equivalence of algebraic K-theories”, Journal of Pure and Applied Algebra, 11:1-3 (1977), 245
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
7. Marc Levine, “Relative MilnorK-theory”, K-Theory, 6:2 (1992), 113
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