# Definition:Finitely Generated Module

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## Contents

## Definition

Let $R$ be a ring.

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

Then $G$ is **finitely generated** if and only if there is a generator for $G$ which is finite.

## Also known as

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

## Also see

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 27$