Alphabeta MathDivisibility, Euclidean Domains, Principal Ideal Domains and Unique Factorisation
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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.
✓ 2 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 2 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
2 · Logical flowchart
3 · Items
Definition
Divisibility and associates in an integral domain
Definition
Irreducible and prime elements of an integral domain
Definition
Euclidean domain and Euclidean function
Definition
Principal ideal domain
Definition
Unique factorisation domain
Theorem
Every Euclidean domain is a principal ideal domain
Lemma