Geodesic
Modules in which every surjective endomorphism has a $\delta$-small kernel
Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 170-189

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\delta$-Hopfian. Also, we show that for a ring $R$, $\delta(R)=J(R)$ if and only if for all $R$-modules, the conditions $\delta$-Hopfian and generalized Hopfian are equivalent. Moreover, we prove that $\delta$-Hopfian property is a Morita invariant. Further, the $\delta$-Hopficity of modules over truncated polynomial and triangular matrix rings are considered.
Keywords: Dedekind finite modules, generalized Hopfian modules, $\delta$-Hopfian modules.
Mots-clés : Hopfian modules 
@article{ADM_2018_26_2_a1,
     author = {Shahabaddin Ebrahimi Atani and Mehdi Khoramdel and Saboura Dolati Pishhesari},
     title = {Modules in which every surjective endomorphism has a $\delta$-small kernel},
     journal = {Algebra and discrete mathematics},
     pages = {170--189},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a1/}
}
TY  - JOUR
AU  - Shahabaddin Ebrahimi Atani
AU  - Mehdi Khoramdel
AU  - Saboura Dolati Pishhesari
TI  - Modules in which every surjective endomorphism has a $\delta$-small kernel
JO  - Algebra and discrete mathematics
PY  - 2018
SP  - 170
EP  - 189
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a1/
LA  - en
ID  - ADM_2018_26_2_a1
ER  - 
%0 Journal Article
%A Shahabaddin Ebrahimi Atani
%A Mehdi Khoramdel
%A Saboura Dolati Pishhesari
%T Modules in which every surjective endomorphism has a $\delta$-small kernel
%J Algebra and discrete mathematics
%D 2018
%P 170-189
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a1/
%G en
%F ADM_2018_26_2_a1
Shahabaddin Ebrahimi Atani; Mehdi Khoramdel; Saboura Dolati Pishhesari. Modules in which every surjective endomorphism has a $\delta$-small kernel. Algebra and discrete mathematics, Tome 26 (2018) no. 2, pp. 170-189. http://geodesic.mathdoc.fr/item/ADM_2018_26_2_a1/