This article is cited in 16 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.

UDC: 513.836

MSC: Primary 18F25; Secondary 16A54

Received: 27.07.1970

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

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