Theorems · Definition · commutative algebra

algEquivEquivAlgHom

(K : Type u_1) →
  (L : Type u_2) →
    [inst : Field K] → [inst_1 : Field L] → [inst_2 : Algebra K L] → [FiniteDimensional K L] → Gal(L/K) ≃* (L →ₐ[K] L)

Bijection between algebra equivalences and algebra homomorphisms

Defined in: Mathlib.RingTheory.Algebraic.Integral
Cited by: 3 results in Mathlib
Foundations: Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra FiniteDimensional

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Cites7

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

Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
AlgHomstatement · cited by 3,236
FiniteDimensionalstatement and proof · cited by 1,854
AlgEquivstatement · cited by 1,681
MulEquivstatement · cited by 1,142
Algebra.IsAlgebraic.algEquivEquivAlgHomproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

IntermediateField.fixingSubgroup_fixedFieldproof · cited by 3
IsGalois.IntermediateField.AdjoinSimple.card_aut_eq_finrankproof · cited by 1
AlgEquiv.card_leproof · cited by 0