STATE SPACES OF K0 GROUPS OF SOME RINGS

Let R be a ring with the Jacobson radical J(R) and let pi: R -> R/J(R) be the canonical map. Then pi induces an order preserving group homomorphism K-0 pi : K-0(R)-> K-0(R/J(R)) and an affine continuous map S(K-0 pi) between the state space St(R/J(R)) and the state space St(R). In this paper, we consider the natural affine map S(K-0 pi). We give a condition under which S(K-0 pi) is an affine homeomorphism. At the same time, we discuss the relationship between semilocal rings and semiperfect rings by using the affine map S(K-0 pi).