Modules in which every surjective endomorphism has a \(\delta\)-small kernel

• Date: 2019
• Main Authors: Ebrahimi Atani, Shahabaddin, Khoramdel, Mehdi, Dolati Pishhesari, Saboura
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: Dedekind finite modules; Hopfian modules; generalized Hopfian modules; \(\delta\)-Hopfian modules; 16D10; 16D40; 16D90
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/365
• Journal Title: Algebra and Discrete Mathematics

In this paper, we introduce the notion of \(\delta\)-Hopfian modules. We give some properties  of these modules and provide a~characterization of semisimple rings in terms of \(\delta\)-Hopfian modules by  proving  that a ring \(R\) is semisimple if and only if every  \(R\)-module is \(\delta\)-Hopf...