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Title: | Modules in which every surjective endomorphism has a δ-small kernel |
Authors: | Atani, S.E. Khoramdel, M. Pishhesar, S.D. |
Keywords: | Dedekind finite modules Hopfian modules generalized Hopfian modules δ-Hopfian modules |
Issue Date: | 2018 |
Publisher: | ДЗ "ЛНУ імені Тараса Шевченка" |
Series/Report no.: | математичні науки; |
Abstract: | Hopfian modules, δ-Hopfian modules. 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. |
Description: | Atani S.E. Modules in which every surjective endomorphism has a δ-small kernel / S.E. Atani, M.Khoramde , ,S.D.Pishhesari // Algebra and Discrete Mathematics. - 2018. - Vol. 26. - Number 2. - Рp. 170-189 |
URI: | http://hdl.handle.net/123456789/4549 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 2 (26). - 2018 |
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