Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.of_map_maximalIdeal
∀ {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.IsSeparable (IsLocalRing.ResidueField R) (IsLocalRing.ResidueField S)],
Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R) = IsLocalRing.maximalIdeal S → Algebra.FormallyUnramified R S[Stacks Tag 02FM](https://stacks.math.columbia.edu/tag/02FM)
- Defined in
- Mathlib.RingTheory.Unramified.LocalRing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- add_zeroproof · cited by 2,707
- TensorProductproof · cited by 2,545
- map_zeroproof · cited by 1,614
- Submodule.spanproof · cited by 1,504
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_map_maximalIdeal_eqproof · cited by 2