Commutative algebra Domains and factorization Concept
Integral domain
Summary
An integral domain is a nonzero commutative ring in which the product of two nonzero elements is never zero. The integers are the model example. The definition of an integral domain gives the conditions.
Where this leads
19 pages build on this one.
- Regular local rings are UFDs
- Krull intersection theorem
- Dedekind domain
- Integrally closed domain
- Discrete valuation ring
- Integral extensions of fields
- Integral scheme
- Fractional ideal
- Integral closure
- Coordinate ring
- Characterizations of discrete valuation rings
- Semistable reduction theorem
- Incomparability theorem
- Order (ring theory)
- Invertible ideal
- Regular local rings are domains
- Nagata ring
- Going-down theorem
- Bareiss algorithm
Further reading
- Web https://en.wikipedia.org/wiki/Integral_domain, lead section
About this page
| Tag | 0QVD7WBFGN |
|---|---|
| URI | m2://0QVD7WBFGN |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13G05 |
| Specializes | Commutative ring |
| 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
Special cases
- Unique factorisation domain
- Prüfer domain
- Mori domain
- Dedekind domain
- GCD domain
- Krull domain
- Atomic domain
- Integrally closed domain
- Valuation ring
Used by
- Krull intersection theorem
- Dedekind domain
- Integrally closed domain
- Discrete valuation ring
- Integral extensions of fields
- Integral scheme
- Fractional ideal
- Integral closure
- Coordinate ring
- Characterizations of discrete valuation rings
- Order (ring theory)
- Invertible ideal
- Regular local rings are domains
- Nagata ring
- Going-down theorem
- Bareiss algorithm