  In this paper, we prove an extension of Zaks' conjecture on integral domains
with semi-regular proper homomorphic images (with respect to finitely generated
ideals) to arbitrary rings (i.e., possibly with zero-divisors). The main result
extends and recovers Levy's related result on Noetherian rings and Matlis'
related result on Prufer domains. It also globalizes Couchot's related result
on chained rings. New examples of rings with semi-regular proper homomorphic
images stem from the main result via trivial ring extensions.
