Theorems · Theorem · commutative algebra
Ideal.inertiaDeg_below_le
∀ {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.IsPrime] [r.LiesOver q] [Module.Finite R T], q.inertiaDeg R ≤ r.inertiaDeg R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Module.Finitestatement and proof · cited by 1,032
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.inertiaDegstatement · cited by 60
- Ideal.inertiaDeg_posproof · cited by 8
- Ideal.inertiaDeg_below_dvdproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.inertiaDeg'_below_leproof · cited by 0