Geodesic
Retractable and coretractable modules
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 2, pp. 5-20.

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In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and their interrelations. Right fully Kasch rings are described. It is proved that for a module $M$ of finite length, the following conditions are equivalent. (1) In the category $\sigma(M)$, every module is retractable. (2) In the category $\sigma(M)$, every module is coretractable. (3) $M$ is a CSL-module. (4) $\mathrm{Ext}_R^1(S_1,S_2)=0$ for any two simple nonisomorphic modules $S_1,S_2\in\sigma(M)$. (5) $M$ is a fully Kasch module. 
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A. N. Abyzov; A. A. Tuganbaev. Retractable and coretractable modules. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 2, pp. 5-20. http://geodesic.mathdoc.fr/item/FPM_2014_19_2_a0/

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