On a question posed by C. Weibel on surjectivity in algebraic \(K\)-theory (Q1176654)

The author proves that if \(\hbox{nil}(R)\) is the nilradical of \(R\), then there are isomorphisms of the form \[ K_ n(R)\cong K_ n(R,\hbox{nil}(R))\otimes K_ n(R/\hbox{nil}(R)) \] for all \(n\geq 0\) in the cases when either (a) \(R\) is finite or (b) \(R\) is a finite- dimensional \(K\)-algebra where \(\text{char}(K)=0\) or \(K\) is perfect.