Commutative algebra Basic notions Concept
Minimal prime ideal
Summary
A minimal prime ideal of a commutative ring is a prime ideal that contains no smaller prime ideal. Every prime ideal contains a minimal prime, and the nilradical is the intersection of the minimal primes. Geometrically, the minimal primes correspond to the irreducible components of the spectrum. A Noetherian ring has only finitely many minimal primes.
Where this leads
3 pages build on this one.
Further reading
About this page
| Tag | S2D8823P8B |
|---|---|
| URI | m2://S2D8823P8B |
| Kind | concept |
| Writing | W0 stub |
| MSC | 13A15 |
| Specializes | Prime ideal |
| Same as | |
| Changed | 2 November 2026 |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- an inventory row: the row of the inventory that the node accounts for (0 of 1)
- 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.