DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-08-29

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.

Integral ring maps and integral extensions

Definition

Let $f : A \to B$ be a homomorphism of commutative rings. The map $f$ is an integral ring map when every element of $B$ is integral over $A$ in the sense of Integral elements over a commutative ring and algebraic integers. When $A$ is identified with a subring of $B$ , one also says that $B$ is an integral extension of $A$ and writes $A \subseteq B$ integral.

Depends on

Integral elements over a commutative ring and algebraic integers

Integral ring maps and integral extensions

Definition

Depends on

Dependency tree · 2 levels

Sources