Modules in which every surjective endomorphism has a -small kernel
SE Atani, M Khoramdel… - Algebra and Discrete …, 2019 - admjournal.luguniv.edu.ua
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\(\delta\) …
of these modules and provide a~ characterization of semisimple rings in terms of\(\delta\) …
Modules whose surjective endomorphisms have a -small kernels
A El Moussaouy, MH Ziane - Algebraic Structures and Their …, 2022 - as.yazd.ac.ir
In this paper, we introduce a proper generalization of that of Hopfian modules, called
$\gamma $-Hopfian modules. A right $ R $-module $ M $ is said to be $\gamma $-Hopfian, if …
$\gamma $-Hopfian modules. A right $ R $-module $ M $ is said to be $\gamma $-Hopfian, if …
[PDF][PDF] Notes on Generalizations of Hopfian and co-Hopfian modules
A El Moussaouy, M Ziane - Jordan J. Math. Stat, 2022 - journals.yu.edu.jo
A module M is called semi co-Hopfian (resp. semi Hopfian) if any injective (resp. surjective)
endomorphism of M has a direct summand image (resp. kernel). We show that if M is semi …
endomorphism of M has a direct summand image (resp. kernel). We show that if M is semi …
Modules in which every surjective endomorphism has a -small kernel
A El Moussaouy, MH Ziane - ANNALI DELL'UNIVERSITA'DI FERRARA, 2020 - Springer
In this paper we introduce the notion of μ μ-Hopfian modules which is a proper
generalization of that of Hopfian modules. We give some characterizations and properties of …
generalization of that of Hopfian modules. We give some characterizations and properties of …
Jacobson Hopfian modules
A El Moussaouy… - Algebra and Discrete …, 2022 - admjournal.luguniv.edu.ua
The study of modules by properties of their endomorphisms has long been of interest. In this
paper we introduce a proper generalization of that of Hopfian modules, called Jacobson …
paper we introduce a proper generalization of that of Hopfian modules, called Jacobson …
[PDF][PDF] Generalizations of Hopfian and co-Hopfian modules
Y Wang - … journal of mathematics and mathematical sciences, 2005 - kurims.kyoto-u.ac.jp
Let R be a ring and M a left R-module. M which satisfies DCC on essential submodules is
GCH, and M which satisfies ACC on small submodules is WH. If M [X] is GCH R [X]-module …
GCH, and M which satisfies ACC on small submodules is WH. If M [X] is GCH R [X]-module …
[PDF][PDF] Hopfcity and Jacobson small submodules
A El Moussaouy - Algebraic Structures and Their Applications, 2023 - as.yazd.ac.ir
The study of modules by properties of their endomorphisms has long been of interest. In this
paper, we introduce the notion of jacobson weakly Hopfian modules. It is shown that over a …
paper, we introduce the notion of jacobson weakly Hopfian modules. It is shown that over a …
[PDF][PDF] On hopfian and co-hopfian modules
Y Gang, L Zhong-kui - Vietnam J. Math, 2007 - researchgate.net
Ar-module M is said to be Hopfian (respectively Co-Hopfian) in case any surjective
(respectively injective) R-homomorphism is automatically an isomorphism. In this paper we …
(respectively injective) R-homomorphism is automatically an isomorphism. In this paper we …
[PDF][PDF] Some properties of endomorphism of modules
A El Moussaouy, MH Ziane - Palestine Journal of Mathematics, 2022 - pjm.ppu.edu
An R-module M is called weakly Hopfian (respectively generalized co-Hopfian) if for every
small epimorphism (respectively essential monomorphism) f of M is isomorphism. If M is …
small epimorphism (respectively essential monomorphism) f of M is isomorphism. If M is …
Notes on generalized Hopfian and weakly co-Hopfian modules
Y Gang, L Zhongkui - Communications in Algebra®, 2010 - Taylor & Francis
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