JP Journal of Algebra, Number Theory and Applications
Volume 47, Issue 1, Pages 15 - 29
(July 2020) http://dx.doi.org/10.17654/NT047010015 |
|
ON e-SMALL RETRACTABLE MODULES
Serigne Moussa Diakhate, Abdoul Djibril Diallo, Papa Cheikhou Diop and Mamadou Barry
|
Abstract: Let R be a commutative ring and M be a unital R-module. A submodule N of M is called e-small submodule of M if, for any essential submodule L of M, N + L = M implies L = M. An R-module M is called e-small retractable if Hom(M, N) = 0 for each non-zero e-small submodule N of M. In this paper we introduce the concept of e-small retractable modules as a generalisation of retractable modules, and give some of their properties, characterizations and examples. Also semi-simple artinian rings and perfect are characterized in terms of e-small retractable modules. Another hand we study the relations between e-small retractable modules and other related modules. |
Keywords and phrases: e-small submodules, retractable modules, e-small retractable modules, artinian rings.
|
|
Number of Downloads: 226 | Number of Views: 675 |
|