Zaks' conjecture on rings with semi-regular proper homomorphic images

摘要

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