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

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• 作者：K. Adarbeh ^{khalidwa@kfupm.edu.sa" class="auth_mail" title="E-mail the corresponding author} ; S. Kabbaj ; ^{kabbaj@kfupm.edu.sa" class="auth_mail" title="E-mail the corresponding author}
• 关键词：13C10 ; 13C11 ; 13E05 ; 13F05 ; 13H10 ; 16A30 ; 16A50 ; 16A52
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：466
• 期：Complete
• 页码：169-183
• 全文大小：365 K

文摘

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.