Theorems · Theorem · commutative algebra

Ideal.relNorm_eq_pow_of_isPrime_isGalois

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDomain R] {S : Type u_3} [inst_2 : CommRing S] [inst_3 : IsDomain S]
  [inst_4 : IsIntegrallyClosed R] [inst_5 : IsIntegrallyClosed S] [inst_6 : Algebra R S] [inst_7 : Module.Finite R S]
  [inst_8 : Module.IsTorsionFree R S] [inst_9 : IsDedekindDomain R] [inst_10 : IsDedekindDomain S] (P : Ideal S)
  (p : Ideal R) [hPp : P.LiesOver p] [p.IsMaximal] [P.IsPrime] [IsGalois (FractionRing R) (FractionRing S)],
  (Ideal.relNorm R) P = p ^ P.inertiaDeg R

See Ideal.relNorm_eq_pow_of_isMaximal for a statement that does not require the extension to be Galois.

Defined in: Mathlib.RingTheory.Ideal.Norm.RelNorm
Cited by: 1 results in Mathlib
Foundations: Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain CommRing IsDomain IsIntegrallyClosed IsIntegrallyClosed Algebra Module.Finite Module.IsTorsionFree IsDedekindDomain IsDedekindDomain Ideal.LiesOver Ideal.IsMaximal Ideal.IsPrime IsGalois

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DFunLike.coestatement and proof · cited by 62,936
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Idealstatement and proof · cited by 4,748
Bot.botproof · cited by 4,720
Finset.prodproof · cited by 2,356
Finset.cardproof · cited by 2,327
mul_commproof · cited by 2,262
IsDomainstatement and proof · cited by 2,196
Module.finrankproof · cited by 1,770
AlgEquivproof · cited by 1,681
LT.lt.ne'proof · cited by 1,417

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Ideal.relNorm_eq_pow_of_isMaximalproof · cited by 1