Geodesic
Euclidean Modules
Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 937-946

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In this paper, we introduce the notion of Euclidean module and weakly Euclidean ring. We prove the main result that a commutative ring $R$ is weakly Euclidean if and only if every cyclic $R$-module is Euclidean, and also if and only if $\operatorname{End}({}_{R}M)$ is weakly Euclidean for each cyclic $R$-module $M$. In addition, some properties of torsion-free Euclidean modules are presented.
Mots-clés : Euclidean modules, torsion-free Euclidean modules.
Keywords: weakly Euclidean rings 
@article{MZM_2014_95_6_a13,
     author = {Jichun Liu and Miaosen Chen},
     title = {Euclidean {Modules}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {937--946},
     publisher = {mathdoc},
     volume = {95},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a13/}
}
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Jichun Liu; Miaosen Chen. Euclidean Modules. Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 937-946. http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a13/