Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.iff_map_maximalIdeal_eq
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : IsLocalRing R] [inst_4 : IsLocalRing S] [inst_5 : IsLocalHom (algebraMap R S)] [Algebra.EssFiniteType R S],
Algebra.FormallyUnramified R S ↔
Algebra.IsSeparable (IsLocalRing.ResidueField R) (IsLocalRing.ResidueField S) ∧
Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R) = IsLocalRing.maximalIdeal S- Defined in
- Mathlib.RingTheory.Unramified.LocalRing
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Ideal.mapstatement and proof · cited by 692
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealstatement and proof · cited by 297
- Algebra.IsSeparablestatement and proof · cited by 210
- IsLocalRing.ResidueFieldstatement and proof · cited by 156
- IsLocalHomstatement and proof · cited by 100
- Algebra.FormallyUnramifiedstatement and proof · cited by 75
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_eq_one_iffproof · cited by 4
- Algebra.isUnramifiedAt_iff_map_eqproof · cited by 2