DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-07

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.

The absolute norm of an integral ideal

Definition

For a nonzero integral ideal $a \subseteq O_{K}$ , define its absolute norm by $N a = ∣ O_{K} / a ∣$ . The next lemma establishes that this cardinality is finite.

Used by

The norm of a prime ideal Corollary
Ideal norm is multiplicative Theorem
The discriminant is the norm of the different Theorem
The norm of a principal integral ideal Theorem

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

J. S. Milne, Algebraic Number Theory, Chapter 4 (standard reference, not scraped)