Finitely generated flat modules and a characterization of semiperfect rings

摘要

For a ring S let K-0(FGFl(S)) and K-0(FGPr(S)) denote the Grothendieck groups of the category of all finitely generated flat S-modules and the category of all finitely generated projective S-modules respectively. We prove that a semilocal ring R is semiperfect if and only if the group homomorphism K-0(FGFl(R)) --> K-0(FGFl(R/J(R))) is an epimorphism and K-0(FGFl(R)) = K-0(FGPr(R)). [References: 24]