Modules in which every surjective endomorphism has a δ-small kernel

• Published in: Algebra and Discrete Mathematics
• Date: 2018
• Main Authors: Ebrahimi Atani, S., Khoramdel, M., Dolati Pishhesari, S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188409
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Modules in which every surjective endomorphism has a δ-small kernel / S. Ebrahimi Atani, M. Khoramdel, S. Dolati Pishhesari // Algebra and Discrete Mathematics. — 2018. — Vol. 26, № 2. — С. 170–189. — Бібліогр.: 18 назв. — англ.

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