---
tag: 05QY1VEBYD
kind: concept
name: Finitely generated module
msc: ["13E15", 16D10]
sources:
  - url: https://en.wikipedia.org/wiki/Finitely_generated_module
    locator: Definition
same_as:
  wikidata: Q1340572
  wikipedia: Finitely generated module
---

## Summary

A finitely generated module is a module in which every element is a linear combination of a fixed finite set of elements.