Extensions of exchange rings

We define non-unital exchange rings and we prove that if I is an ideal of a ring R, then R is an exchange ring if and only if I and R/I are exchange rings and idempotents can be lifted module I. We also show that we can replace the condition on liftability of idempotents with the condition that the canonical map K-0(R) --> K-0(R/I) be sujective. (C) 1997 Academic Press.