STATE SPACES OF K0 GROUPS OF SOME RINGS

‎Let R be a ring‎ ‎with the Jacobson radical J(R) and let π:R→R/J(R) be‎ the canonical map‎. ‎Then π induces an order preserving group homomorphism‎ ‎K0π:K0(R)→K0(R/J(R)) and an‎ ‎affine continuous map S(K0π) between the state space St(R/J(R)) and the‎ ‎state space St(R).‎ ‎In this paper‎, ‎we consider the natural affine map S(K0π). We give a condition under which S(K0π) is‎ ‎an affine homeomorphism‎. ‎At the same time‎, ‎we discuss the relationship between semilocal rings and semiperfect rings by using the‎ ‎affine map S(K0π).