Commutative algebra Domains and factorization Concept
Field of fractions
Summary
The field of fractions of an integral domain is the smallest field that contains it. Its elements are the fractions with . The rational numbers are the field of fractions of the integers. The definition of the field of fractions gives the construction.
Where this leads
16 pages build on this one.
- Dedekind domain
- Integrally closed domain
- Mikusiński field of operators
- Discrete valuation ring
- Integral scheme
- Fractional ideal
- Integral closure
- Semistable reduction theorem
- Posner's theorem
- Proper morphism
- Order (ring theory)
- Valuative criterion
- Invertible ideal
- Normalization
- Function field of a variety
- Nagata ring
Further reading
- Web https://en.wikipedia.org/wiki/Field_of_fractions, lead section
About this page
| Tag | 0F2PTGX1A2 |
|---|---|
| URI | m2://0F2PTGX1A2 |
| Aliases | fraction-field, quotient-field |
| Kind | concept |
| Writing | W1 stated |
| MSC | 13B30 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (1 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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