Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Rings of integers are Dedekind domains
Statement
Assume the Axiom of Choice. The ring of integers of every number field is a Dedekind domain.
Facts & Assumptions
Given: The Axiom of Choice and a number field .
Assuming Choice, the integral closure of a Dedekind domain in a finite separable extension is Dedekind (The integral closure of a Dedekind domain in a finite separable extension is Dedekind).
Proof
Apply [F1] with base ring and extension .
Its integral closure is precisely , so it is Dedekind.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
11 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Milne, Theorem 3.1 (standard reference, not scraped)