All Questions

Let $R$ be a ring (not necessary commutative) and let $P_{\bullet}$ be a perfect $R$-bimodule (chain complex). I will denote the category of perfect right $R$-chain complexes by $\textbf{Perf}(R)$. ...

I suppose this is a question with a well known answer. Suppose $A$ and $B$ are two algebras over some field and there is a map $$ f: \operatorname{K_0}(A) \to \operatorname{K_0}(B) $$ is it ...