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.
A finite field extension is simple if and only if it has finitely many intermediate fields
Statement
A finite field extension is simple if and only if it has finitely many intermediate fields.
Facts & Assumptions
Given: A finite field extension .
A simple finite extension has only finitely many intermediate fields (A simple finite extension has only finitely many intermediate fields).
A finite extension with only finitely many intermediate fields is simple (A finite extension with only finitely many intermediate fields is simple).
Proof
If is simple, [L1] gives finitely many intermediate fields.
If has finitely many intermediate fields, [L2] makes it simple.
Steps 1.1 and 1.2 prove both directions of the equivalence.
Depends on
Used by
Dependency tree · two levels
9 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
- P. L. Clark, Field Theory, Chapter 5 (standard reference, not scraped)
- J. S. Milne, Fields and Galois Theory, Chapter 5 (standard reference, not scraped)