Extensions of exchange rings

Abstract

We define non-unital exchange rings and we prove that ifIis an ideal of a ringR, thenRis an exchange ring if and only ifIandR/Iare exchange rings and idempotents can be lifted moduloI. We also show that we can replace the condition on liftability of idempotents with the condition that the canonical mapK0(R)→K0(R/I) be surjective. © 1997 Academic Press.