Theorems · Theorem · commutative algebra
Ideal.inertiaDeg_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], r.inertiaDeg R = q.inertiaDeg R * r.inertiaDeg S- Cited by
- 7 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Module.finrankproof · cited by 1,770
- Ideal.IsPrimeproof · cited by 827
- Localization.AtPrimeproof · cited by 299
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.underproof · cited by 170
- Ideal.ResidueFieldproof · cited by 119
- Ideal.inertiaDegstatement and proof · cited by 60
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg_above_dvdproof · cited by 2
- Ideal.inertiaDeg_below_dvdproof · cited by 2
- Ideal.absNorm_relNormproof · cited by 2
- Ideal.relNorm_eq_pow_of_isMaximalproof · cited by 1
- IsDecompositionField.inertiaDeg_eqproof · cited by 0
- Ideal.inertiaDegIn_mul_inertiaDegInproof · cited by 0
- Ideal.inertiaDeg'_towerproof · cited by 0