Pure submodule
= Pure submodule
{wiki=Pure_submodule}
In the context of module theory, a **pure submodule** is a specific type of submodule that satisfies a certain property related to the lifting of elements in modules. Let’s break down the definition and its significance. Let \\( R \\) be a ring, and let \\( M \\) be an \\( R \\)-module.