Definition:Finitely Generated Module

Definition

Let $R$ be a ring.

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

Then $M$ is finitely generated if and only if 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

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases