Theorems · Theorem · commutative algebra
Ideal.ramificationIdx_def
∀ {S : Type u_1} [inst : CommRing S] (q : Ideal S) (R : Type u_2) [inst_1 : CommRing R] [inst_2 : Algebra R S]
[inst_3 : q.IsPrime],
q.ramificationIdx R =
(Module.length (Localization.AtPrime q)
(Localization.AtPrime q ⧸ Ideal.map (algebraMap R (Localization.AtPrime q)) (Ideal.under R q))).toNat- Cited by
- 6 results in Mathlib
- Foundations
- Depth 84 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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement · cited by 4,706
- HasQuotient.Quotientstatement · cited by 2,301
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement · cited by 692
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- Ideal.understatement · cited by 170
- ENat.toNatstatement · cited by 143
Cited by6
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_eqproof · cited by 6
- Ideal.ramificationIdx_posproof · cited by 5
- Ideal.ramificationIdx_eq_one_iffproof · cited by 4
- Ideal.ramificationIdx_eq_oneproof · cited by 3
- Ideal.ramificationIdx_tower'proof · cited by 2
- Ideal.ramificationIdx'_defproof · cited by 0