Further Results on Finitely Generated Projective Modules

Abstract

In this paper, the exchange rings R whose primitive factor rings are artinian are studied. The following results are proved: for any exchange ring R and any two-sided ideal I of R, K0(π) : K0(R)→K0(R/I) is a group epimorphism with the kernel {[P]−[Q] |P = PI, Q = QI}; there is an isomorphism of ordered groups from K0(R) to the gorup of all such functions ƒP : X→Q(P∈p(R)), where X is the set of all primitive ideals of R and Q, the rational integers.