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Mat. Zametki, 2014, Volume 95, Issue 6, Pages 937–946 (Mi mz10455)  

Euclidean Modules

Jichun Liuab, Miaosen Chenc

a Zhejiang University
b Fujian Jiangxia University
c Zhejiang Normal University

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 $\operatorname{End}( _{R}M)$ is weakly Euclidean for each cyclic $R$-module $M$. In addition, some properties of torsion-free Euclidean modules are presented.

Keywords: Euclidean modules, weakly Euclidean rings, torsion-free Euclidean modules.

DOI: https://doi.org/10.4213/mzm10455

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English version:
Mathematical Notes, 2014, 95:6, 865–872

Bibliographic databases:

UDC: 512.533
Received: 04.06.2012
Revised: 15.03.2013

Citation: Jichun Liu, Miaosen Chen, “Euclidean Modules”, Mat. Zametki, 95:6 (2014), 937–946; Math. Notes, 95:6 (2014), 865–872

Citation in format AMSBIB
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\paper Euclidean Modules
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\vol 95
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\pages 937--946
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\issue 6
\pages 865--872
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