ALGEBRAICK-THEORY AS EXTRAORDINARY HOMOLOGY THEORY ON THE CATEGORY OF ASSOCIATIVE RINGS WITH UNITY

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.