Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.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] [IsLocalHom (algebraMap R S)] [Algebra.EssFiniteType R S]
[Algebra.FormallyUnramified R S], Ideal.map (algebraMap R S) (IsLocalRing.maximalIdeal R) = IsLocalRing.maximalIdeal S[Stacks Tag 00UW](https://stacks.math.columbia.edu/tag/00UW) ((1))
- Defined in
- Mathlib.RingTheory.Unramified.LocalRing
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 182 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 · 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
- IsLocalHomstatement and proof · cited by 100
- Algebra.FormallyUnramifiedstatement and proof · cited by 75
- Algebra.EssFiniteTypestatement and proof · cited by 68
- IsLocalRing.eq_maximalIdealproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx_eq_oneproof · cited by 3
- Algebra.FormallyUnramified.iff_map_maximalIdeal_eqproof · cited by 2
- IsLocalRing.adjoin_residue_eq_top_iff_adjoin_eq_topproof · cited by 2
- IsLocalRing.finrank_eq_finrank_residueFieldproof · cited by 1
- Localization.localRingHom_surjective_of_primesOver_eq_singletonproof · cited by 1