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.

e-small submodules, retractable modules, e-small retractable modules, artinian rings.