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Theorems · Definition · number theory

RingOfIntegers.monicFactorsMod

{K : Type u_1} →
  [inst : Field K] → NumberField.RingOfIntegers K → (p : ℕ) → [inst : Fact (Nat.Prime p)] → Finset (Polynomial (ZMod p))

The finite set of monic irreducible factors of minpoly ℤ θ modulo p.

Defined in
Mathlib.NumberTheory.NumberField.Ideal.KummerDedekind
Cited by
10 results in Mathlib
Foundations
Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldFact

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.Ideal.primesOverSpanEquivMonicFactorsMod · cited by 10Ideal.primesOverSpanEquiv…NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_span · cited by 2Ideal.primesOverSpanEquiv…NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply · cited by 1Ideal.inertiaDeg_primesOv…NumberField.Ideal.inertiaDeg_primesOverSpanEquivMonicFactorsMod_symm_apply' · cited by 1Ideal.inertiaDeg_primesOv…NumberField.Ideal.liesOver_primesOverSpanEquivMonicFactorsMod_symm · cited by 1Ideal.liesOver_primesOver…NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply · cited by 1Ideal.ramificationIdx_pri…NumberField.Ideal.ramificationIdx_primesOverSpanEquivMonicFactorsMod_symm_apply' · cited by 1Ideal.ramificationIdx_pri…RingOfIntegers.ZModXQuotSpanEquivQuotSpanPair · cited by 1RingOfIntegers.ZModXQuotS…IsCyclotomicExtension.Rat.inertiaDeg_eq_of_not_dvd · cited by 1Rat.inertiaDeg_eq_of_not_…IsCyclotomicExtension.Rat.ramificationIdx_eq_of_not_dvd · cited by 1Rat.ramificationIdx_eq_of…NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply · cited by 0Ideal.primesOverSpanEquiv…NumberField.Ideal.primesOverSpanEquivMonicFactorsMod.congr_simp · cited by 0primesOverSpanEquivMonicF…Finset · cited by 13712FinsetField · cited by 7404FieldPolynomial · cited by 5681PolynomialFact · cited by 2726FactNat.Prime · cited by 2059Nat.PrimeZMod · cited by 1024ZModPolynomial.map · cited by 806Polynomial.mapminpoly · cited by 439minpolyNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersInt.castRingHom · cited by 254Int.castRingHomMultiset.toFinset · cited by 230Multiset.toFinsetUniqueFactorizationMonoid.normalizedFactors · cited by 151UniqueFactorizationMonoid…RingOfIntegers.monicFactorsModCITED BYCITES

Cites12

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

Cited by12

Results whose statement or proof uses this declaration.