Alphabeta MathDefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-31
How 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.
Dedekind domains
Definition
A Dedekind domain is a commutative ring such that:
- is a Noetherian ring (Left and right Noetherian rings);
- is an integrally closed domain (Integral closure in an extension ring and integrally closed domains);
- has Krull dimension (Krull dimension of a nonzero ring).
Thus this page uses the one-dimensional normal-domain convention, so fields are excluded.