Theorems · Theorem · number theory
IsCyclotomicExtension.splits_cyclotomic
∀ {n : ℕ} [NeZero n] {S : Set ℕ} (K : Type w) (L : Type z) [inst : Field K] [inst_1 : Field L] [inst_2 : Algebra K L]
[IsCyclotomicExtension S K L], n ∈ S → (Polynomial.map (algebraMap K L) (Polynomial.cyclotomic n K)).SplitsA cyclotomic extension splits cyclotomic n K if n ∈ S.
- Defined in
- Mathlib.NumberTheory.Cyclotomic.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- Finset.prodproof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
- IsCyclotomicExtensionstatement and proof · cited by 220
- Polynomial.cyclotomicstatement and proof · cited by 130
- NeZero.posproof · cited by 57
Cited by1
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.splitting_field_cyclotomicproof · cited by 0