Multirelative algebraic K-theory: The group \(K_ 2(\Lambda;I_ 1,\dots ,I_ n)\) and related computations
The author defines multirelative algebraic K-theory groups \(K_ i(\Lambda;I_ 1,...,I_ n)\) for \(I_ 1,...,I_ n\) two-sided ideals of a ring \(\Lambda\). He also computes \(K_ 2(\Lambda;I_ 1,...,I_ n)\) when \(I_ 1\cap...\cap I_ n=0\) and in some cases when \(\Lambda\) is commutative and \(I_ 1\cap...\cap I_ n\) is a radical ideal. As an application he computes \(K_ 2(R[x_ 1...x_ n]/(x_ 1...x_ n))\) when R is a regular ring. The results are based on work of \textit{R. Brown} and \textit{J.-L. Loday} [Topology 26, 311-335 (1987; Zbl 0622.55009)].
scientific article; zbMATH DE number 4027726
scientific article