Geodesic
Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity
Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 859-887.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1971_5_4_a7,
     author = {I. A. Volodin},
     title = {Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity},
     journal = {Izvestiya. Mathematics },
     pages = {859--887},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a7/}
}
TY  - JOUR
AU  - I. A. Volodin
TI  - Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity
JO  - Izvestiya. Mathematics 
PY  - 1971
SP  - 859
EP  - 887
VL  - 5
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a7/
LA  - en
ID  - IM2_1971_5_4_a7
ER  - 
%0 Journal Article
%A I. A. Volodin
%T Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity
%J Izvestiya. Mathematics 
%D 1971
%P 859-887
%V 5
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a7/
%G en
%F IM2_1971_5_4_a7
I. A. Volodin. Algebraic $K$-theory as extraordinary homology theory on the category of associative rings with unity. Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 859-887. http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a7/

[1] Atya M., Lektsii po $K$-teorii, Mir, M., 1967 | MR

[2] Borel A., Linear algebraic groups, algebraic groups and discontinuous subgroups, Providence, 1966 | MR

[3] Bass H., “$K$-theory and stable algebra”, Inst. des Hautes Et. Sci., 22 (1964), 5–60 | DOI | MR | Zbl

[4] Bass H., “$K_2$ and sumbol”, Lecture Note in Math., 108 (1969), 1–11 | DOI | MR | Zbl

[5] Bass H., Heller A., Swan R. G., “The Whitehead groups of polynomial extensions”, Inst. Des Hautes Et. Sci., 22 (1964), 61–79 | DOI | MR

[6] Bass H., Schanuel S., “The homotopy theory of projective modules”, Bull. Amer. Math. Soc., 68 (1962), 425–428 | DOI | MR | Zbl

[7] Milnor Dzh., “Kruchenie Uaitkheda”, Matematika, 11:1 (1967), 3–42 | MR

[8] Milnor J., Notes on the algebraic $K$-theory, preprint, Mass. Techn. Inst., 1968 | MR

[9] Novikov S. P., “Algebraicheskoe postroenie i svoistva ermitovykh analogov $K$-teorii nad koltsami s involyutsiei s tochki zreniya gamiltonova formalizma”, Izv. AN SSSR. Ser. matem., 34 (1970), 253–288 ; 475–500 | MR | Zbl | Zbl

[10] Nobile A., Villamayor O. E., “Sur la $K$-théorie algébrique”, Ann. scient. Ecole norm. supér.(4), 1:4 (1968), 581–616 | MR | Zbl

[11] Xu-Sy-Tszyan, Teoriya gomotopii, Mir, M., 1964