---
tag: 0GSW76Q14N
kind: concept
name: Ideal generated by a subset
msc: [13A15]
sources:
  - url: https://en.wikipedia.org/wiki/Ideal_(ring_theory)
    locator: Definitions
---

## Summary

The ideal generated by a subset of a ring is the smallest ideal that contains the subset.
In a commutative ring, it is the set of the finite linear combinations of elements of the subset.
The [[definition of the generated ideal|030TZ0DQWT]] gives the details.