Definition:Finitely Generated Module

Definition
Let $R$ be a ring.

Let $M$ be a module over $R$.

Then $M$ is finitely generated there is a generator for $M$ which is finite.

Also known as
A finitely generated module is also known as a module of finite type.

Also see

 * Definition:Finite Dimensional Free Module
 * Definition:Module of Finite Length
 * Definition:Rank of Module