查看文章

In this article, we introduce some conditions about some concepts in order to obtain injective module ℳ and so any 𝐴 ℳ (ℳ is C1-module). Some cases have been studied to approach our objective such as free and anti-hopfian properties. Every submodule of injective module is essential in ℳ and hence ℳ is C1-module. Also, a module ℳ is C1-module if it does not contain proper essential extension, and we will proof every free R-module ℳ has 𝒩 ℳ. Also, if 𝒩 𝐼ℳ and a module ℳ is faithful, then any 𝒩 ℳ and so ℳ is 𝐶-module.