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Journal of Mathematical Sciences

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

Retractable and Coretractable Modules

  • A. N. Abyzov
  • A. A. Tuganbaev
Article

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) 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.

Keywords

Direct Summand Simple Module Division Ring Indecomposable Module Factor Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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