Theorems · Theorem · commutative algebra
Ideal.ramificationIdx_tower
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] [IsScalarTower R S T] (q : Ideal S) (r : Ideal T)
[r.LiesOver q] [Module.Flat S T], r.ramificationIdx R = q.ramificationIdx R * r.ramificationIdx SSee ramificationIdx_tower' for a version that only assumes local flatness.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- IsScalarTowerstatement and proof · cited by 3,896
- MulZeroClass.mul_zeroproof · cited by 2,091
- Ideal.IsPrimeproof · cited by 827
- Localization.AtPrimeproof · cited by 299
- Module.Flatstatement and proof · cited by 279
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.ramificationIdxstatement and proof · cited by 59
- Localization.AtPrime.algebraOfLiesOverproof · cited by 30
- Ideal.isPrime_of_liesOverproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_above_dvdproof · cited by 2
- Ideal.ramificationIdx_below_dvdproof · cited by 2
- Ideal.ramificationIdxIn_mul_ramificationIdxInproof · cited by 1
- Ideal.ramificationIdx'_towerproof · cited by 0
- IsDecompositionField.ramificationIdx_eqproof · cited by 0