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 [23, Theorem] and Matlis' related result on Prüfer domains [26, Theorem]. It also globalizes Couchot's related result on chained rings [10, Theorem 11]. New examples of rings with semi-regular proper homomorphic images stem from the main result via trivial ring extensions.
| Original language | English |
|---|---|
| Pages (from-to) | 169-183 |
| Number of pages | 15 |
| Journal | Journal of Algebra |
| Volume | 466 |
| DOIs | |
| State | Published - 15 Nov 2016 |
Bibliographical note
Publisher Copyright:© 2016 Elsevier Inc.
Keywords
- Arithmetical ring
- Coherent ring
- Dedekind domain
- IF-ring
- Prüfer domain
- Quasi-Frobenius ring
- Self fp-injective ring
- Semi-regular ring
ASJC Scopus subject areas
- Algebra and Number Theory