Theorems · Theorem · number theory
IsSepClosed.isCyclotomicExtension
∀ (S : Set ℕ) (K : Type w) [inst : Field K] [IsSepClosed K], (∀ a ∈ S, a ≠ 0 → NeZero ↑a) → IsCyclotomicExtension S K K
Separably closed fields are S-cyclotomic extensions over themselves if
NeZero ((a : ℕ) : K) for all nonzero a ∈ S.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Setstatement and proof · cited by 53,352
- Top.topproof · cited by 9,680
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- Set.ofPredproof · cited by 6,101
- Polynomialproof · cited by 5,681
- LT.lt.ne'proof · cited by 1,417
- Polynomial.aevalproof · cited by 615
- Algebra.adjoinproof · cited by 535
- IsCyclotomicExtensionstatement · cited by 220
- Polynomial.cyclotomicproof · cited by 130
- IsSepClosedstatement and proof · cited by 41
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