While the formulations of localization rank and stably free rank are given, the characterizations of elements are obtained for a class of VN regular ring. For a ring R, the characters of some properties of K0R are also given in terms of the state space of K0.
It is shown that a self-injective ring R is coHofian ring if and only if R has stable range one. This answers the open problem 5 of Varadarajian in [9] for self- injective ring R,i.e.,Mn(R) is coHopfian for coHopfian ring R. As a consequence of we answer problem of Goodeal in the affirmative in [3], for self-injective regular rings.
