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JOURNALS // Fundamentalnaya i Prikladnaya Matematika // Archive

Fundam. Prikl. Mat., 2014 Volume 19, Issue 2, Pages 5–20 (Mi fpm1574)

This article is cited in 9 papers

Retractable and coretractable modules

A. N. Abyzova, A. A. Tuganbaevb

a Kazan State University, Kazan, Russia
b National Research University "MPEI", Moscow, Russia

Abstract: 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.

UDC: 512.552


 English version:
Journal of Mathematical Sciences (New York), 2016, 213:2, 132–142

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