Abstract
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 End( R M) is weakly Euclidean for each cyclic R-moduleM. In addition, some properties of torsion-free Euclidean modules are presented.
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Published in Russian in Matematicheskie Zametki, 2014, Vol. 95, No. 6, pp. 937–946.
The text was submitted by the authors in English.
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Liu, J., Chen, M. Euclidean modules. Math Notes 95, 865–872 (2014). https://doi.org/10.1134/S0001434614050319
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DOI: https://doi.org/10.1134/S0001434614050319