Theorems · Theorem · commutative algebra
Ideal.ramificationIdx_eq_one_iff
∀ {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] [Algebra.EssFiniteType R S] [Algebra.IsIntegral R S]
[PerfectField (Ideal.under R q).ResidueField], q.ramificationIdx R = 1 ↔ Algebra.IsUnramifiedAt R q- Cited by
- 4 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- RingHomproof · cited by 10,189
- ENatproof · cited by 4,985
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Nat.cast_oneproof · cited by 2,501
- HasQuotient.Quotientproof · cited by 2,301
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapproof · cited by 692
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement and proof · cited by 299
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx'_eq_one_iffproof · cited by 1
- Algebra.IsUnramifiedIn.ramificationIdx_eq_oneproof · cited by 1
- Algebra.isUnramifiedIn_iff_forall_ramificationIdx_eq_oneproof · cited by 0
- NumberField.exists_not_isUnramifiedAt_int_of_isGaloisproof · cited by 0