Theorems · Theorem · field theory

Algebra.FormallyUnramified.bijective_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],
  Function.Bijective ⇑(algebraMap K A)

Defined in: Mathlib.RingTheory.Unramified.Field
Cited by: 1 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field CommRing Algebra Algebra.FormallyUnramified Algebra.EssFiniteType IsAlgClosed IsLocalRing

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
Moduleproof · cited by 20,661
RingHom.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
Semiringproof · cited by 13,802
AddCommMonoidproof · cited by 12,281
Algebrastatement and proof · cited by 11,388
LinearMapproof · cited by 10,215
RingHomstatement and proof · cited by 10,189
Equivproof · cited by 8,337
Fieldstatement and proof · cited by 7,404
Idealproof · cited by 4,748

Cited by1

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Algebra.FormallyUnramified.isField_of_isAlgClosed_of_isLocalRingproof · cited by 1