Theorems · Theorem · number theory

NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm

∀ {K : Type u_1} [inst : Field K] {θ : NumberField.RingOfIntegers K} {p : ℕ} [inst_1 : Fact (Nat.Prime p)]
  [NumberField K],
  ¬p ∣ RingOfIntegers.exponent θ →
    ∀ {Q : Polynomial ℤ},
      Polynomial.map (Int.castRingHom (ZMod p)) Q ∈ RingOfIntegers.monicFactorsMod θ p →
        (Ideal.span {↑p, (Polynomial.aeval θ) Q}).LiesOver (Ideal.span {↑p})

Defined in: Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind
Cited by: 1 results in Mathlib
Foundations: Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Fact NumberField

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Setstatement · cited by 53,352
Finsetstatement · cited by 13,712
Fieldstatement and proof · cited by 7,404
Polynomialstatement and proof · cited by 5,681
Idealproof · cited by 4,748
Equiv.symmproof · cited by 3,681
AlgHomstatement · cited by 3,236
Factstatement and proof · cited by 2,726
Nat.Primestatement and proof · cited by 2,059
ZModstatement and proof · cited by 1,024
Ideal.spanstatement and proof · cited by 948

Cited by1

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NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_applyproof · cited by 1