Multirelative \(K\)-theory and axioms for the \(K\)-theory of rings (Q1922727)

The author extends his version of higher \(K\)-theory to the multirelative case. The construction is given for a special type of \(m\)-tuples of ideals in non-unital rings (section 6). The multirelative \(K\)-groups fit into natural exact sequences (theorem 1), the \(K\)-groups of free non-unital rings are trivial, and the multirelative \(K_0\) is exactly the Grothendieck group of the intersection of the ideals. In section 7 it is shown that these properties determine all of multirelative \(K\)-theory.