Theorems · Theorem · number theory
IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_prime_pow
∀ {p k : ℕ} {K : Type u} [inst : Field K] {ζ : K} [hp : Fact (Nat.Prime p)] [inst_1 : CharZero K]
[hcycl : IsCyclotomicExtension {p ^ k} ℚ K], IsPrimitiveRoot ζ (p ^ k) → IsIntegralClosure ↥ℤ[ζ] ℤ KIf K is a p ^ k-th cyclotomic extension of ℚ, then (adjoin ℤ {ζ}) is the
integral closure of ℤ in K.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites86
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by4
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePowproof · cited by 5
- IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_applystatement · cited by 1
- IsPrimitiveRoot.adjoinEquivRingOfIntegersOfPrimePow_symm_applystatement · cited by 0
- IsCyclotomicExtension.Rat.isIntegralClosure_adjoin_singleton_of_primeproof · cited by 0