Journal of Mathematical Sciences

, Volume 213, Issue 2, pp 132–142 | Cite as

Retractable and Coretractable Modules

  • A. N. Abyzov
  • A. A. Tuganbaev


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) Ext R 1 (S 1 , S 2) = 0 for any two simple nonisomorphic modules S 1 , S 2σ(M). (5) M is a fully Kasch module.


Direct Summand Simple Module Division Ring Indecomposable Module Factor Ring 
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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Kazan State UniversityKazanRussia
  2. 2.National Research University “MPEI,”MoscowRussia

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