Theorems · Theorem · field theory
Algebra.FormallyUnramified.isField_of_isAlgClosed_of_isLocalRing
∀ (K : Type u_1) (A : Type u_2) [inst : Field K] [inst_1 : CommRing A] [inst_2 : Algebra K A] [Algebra.FormallyUnramified K A] [Algebra.EssFiniteType K A] [IsAlgClosed K] [IsLocalRing A], IsField A
- Defined in
- Mathlib.RingTheory.Unramified.Field
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapproof · cited by 4,706
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
- eq_bot_iffproof · cited by 159
- IsAlgClosedstatement and proof · cited by 150
- Function.Bijective.surjectiveproof · cited by 114
- IsUnit.mapproof · cited by 104
- IsFieldstatement · cited by 103
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.isReduced_of_fieldproof · cited by 6