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.
Why the finite-separable hypothesis is retained in the integral-closure theorem
Remark
The preceding proof is genuinely tied to separability: its key device is the trace-dual basis, and that device collapses once the trace form degenerates. For inseparable extensions the trace can vanish identically, so the argument that traps the integral closure inside one finite trace-dual lattice is no longer available.
This page therefore keeps the exact finite-separable statement. It does not claim any purely inseparable replacement without extra hypotheses on the base domain.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
4 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
- J. P. May, Notes on Dedekind Rings (standard reference, not scraped)
- Mircea Mustata, Introduction to Commutative Algebra, §8.5 (standard reference, not scraped)