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Fundamentalnaya i Prikladnaya Matematika, 2014, Volume 19, Issue 2, Pages 5–20
(Mi fpm1574)
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This article is cited in 9 scientific papers (total 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.
Citation:
A. N. Abyzov, A. A. Tuganbaev, “Retractable and coretractable modules”, Fundam. Prikl. Mat., 19:2 (2014), 5–20; J. Math. Sci., 213:2 (2016), 132–142
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https://www.mathnet.ru/eng/fpm1574 https://www.mathnet.ru/eng/fpm/v19/i2/p5
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Abstract page: | 389 | Full-text PDF : | 173 | References: | 46 |
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