Zaks' conjecture on rings with semi-regular proper homomorphic images
arXiv:1604.03268
Abstract
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.
The condition C2 is slightly modified and Corollary 2.9 and Example 3.2 are added. 14 pages. To appear in Journal of Algebra