The localization sequence in \(K\)-theory
The localization of a ring with respect to a right denominator set of non-zero divisors is shown to induce an exact localization sequence. This 5-term sequence involves the groups \(K_0\) and \(K_1\) of the rings, as well as \(K_0\) of a category of finitely presented torsion modules of projective dimension one. The central localization case had been previously worked out by \textit{Bass}.
finitely presented torsion modules of projective dimension one
scientific article; zbMATH DE number 827894