Email this article Retractable and Coretractable Modules
- Authors: Abyzov A.N.1, Tuganbaev A.A.2
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Affiliations:
- Kazan State University
- National Research University “MPEI,”
- Issue: Vol 213, No 2 (2016)
- Pages: 132-142
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237142
- DOI: https://doi.org/10.1007/s10958-016-2705-5
- ID: 237142
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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 σ(M), every module is retractable. (2) In the category σ(M), every module is coretractable. (3) M is a CSL-module. (4) ExtR1 (S1, S2) = 0 for any two simple nonisomorphic modules S1, S2 ∈ σ(M). (5) M is a fully Kasch module.
About the authors
A. N. Abyzov
Kazan State University
Author for correspondence.
Email: Adel.Abyzov@ksu.ru
Russian Federation, Kazan
A. A. Tuganbaev
National Research University “MPEI,”
Email: Adel.Abyzov@ksu.ru
Russian Federation, Moscow
