Source: wikibot/countably-generated-module
= Countably generated module
{wiki=Countably_generated_module}
In the context of module theory, a module \\( M \\) over a ring \\( R \\) is said to be countably generated if there exists a countable set of elements \\( \\\{ m_1, m_2, m_3, \\ldots \\\} \\) in \\( M \\) such that every element of \\( M \\) can be expressed as a finite \\( R \\)-linear combination of these generators.