Commutative algebra Basic notions Concept
Jacobson radical
Summary
The Jacobson radical of a commutative ring is the intersection of all its maximal ideals. An element lies in it exactly when is a unit for every in the ring. It contains the nilradical, and it is the ideal that appears in Nakayama's lemma. For a local ring it is the unique maximal ideal.
Where this leads
9 pages build on this one.
Further reading
About this page
| Tag | XA0DCNH7WY |
|---|---|
| URI | m2://XA0DCNH7WY |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13A15, 16N20 |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Results about this
Used by
- Nakayama's lemma
- Krull intersection theorem
- Jacobson ring
- Determinant trick
- Completion is flat
- Semi-local ring