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Modules in which every surjective endomorphism has a δ-small kernel
Репозиторій DSpace/Manakin
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Modules in which every surjective endomorphism has a δ-small kernel
Інший ID:
2010 MSC: 16D10, 16D40, 16D90.
Посилання:
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.
Підтримка:
The authors express their deep gratitude to the referee for her/his helpful suggestions for the improvement of this work.
Дата:
2018
Переглядів:
174
Завантажень:
65
Анотація:
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(R) = J(R) if and only if for all R-modules, the conditions δ-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that δ-Hopfian property is a Morita invariant. Further, the δ-Hopficity of modules over truncated polynomial and triangular matrix rings are considered.
