AND THE STABLE RANGE CONDITION OF EXCHANGE RINGS
We prove that for any right R-module Mwith the finite exchange property, has stable range at most nif and only if for any implies xMis isomorphic to the direct summand of Cfor all right R-module C, that an exchange ring Rhas stable range at most nif and only if for any regular element b, implies is a unimodular row in for some and that an exchange ring Ris a GE-ring, if every regular element of Ris unit-regular.
exchange ring, stable range condition, GE-ring.