Theorems · Theorem · commutative algebra
IsLocalization.AtPrime.inertiaDeg_map_eq_inertiaDeg
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (Rₚ : Type u_3) [inst_4 : CommRing Rₚ] [inst_5 : Algebra R Rₚ] [IsLocalization.AtPrime Rₚ p]
[inst_7 : IsLocalRing Rₚ] (Sₚ : Type u_4) [inst_8 : CommRing Sₚ] [inst_9 : Algebra S Sₚ]
[IsLocalization (Algebra.algebraMapSubmonoid S p.primeCompl) Sₚ] [inst_11 : Algebra Rₚ Sₚ] (P : Ideal S)
[hPp : P.LiesOver p] [inst_12 : Algebra R Sₚ] [IsScalarTower R S Sₚ] [IsScalarTower R Rₚ Sₚ] [p.IsMaximal]
[P.IsMaximal] [(Ideal.map (algebraMap S Sₚ) P).LiesOver (IsLocalRing.maximalIdeal Rₚ)],
(IsLocalRing.maximalIdeal Rₚ).inertiaDeg' (Ideal.map (algebraMap S Sₚ) P) = p.inertiaDeg' P- Cited by
- 1 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- HasQuotient.Quotientproof · cited by 2,301
- Module.finrankproof · cited by 1,770
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement and proof · cited by 692
- IsLocalizationstatement and proof · cited by 636
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.primesOverEquivPrimesOver_inertiagDeg_eqproof · cited by 0