Commutative algebra Basic notions Concept
Maximal ideal
Summary
A maximal ideal of a ring is a proper ideal that is not contained in a larger proper ideal. The maximal ideals of are the ideals for prime. The definition of a maximal ideal gives the conditions.
Where this leads
12 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Maximal_ideal, lead section
About this page
| Tag | 0PV74TR5FP |
|---|---|
| URI | m2://0PV74TR5FP |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13A15 |
| Specializes | Prime ideal |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Definitions
Used by
- Jacobson ring
- Dedekind domain
- Faithfully flat module
- Coordinate ring
- Zariski tangent space
- Germ of a smooth function
- Semi-local ring
- Picard group of a ring
- Unique factorization of ideals in a Dedekind domain
- Local ring
- Weak Nullstellensatz