Theorems · Definition · field theory

Field.Emb.Cardinal.embEquivPi

{F : Type u} →
  {E : Type v} →
    [inst : Field F] →
      [inst_1 : Field E] →
        [inst_2 : Algebra F E] →
          [rank_inf : Fact (Cardinal.aleph0 ≤ Module.rank F E)] →
            [inst_3 : Algebra.IsAlgebraic F E] →
              Field.Emb F E ≃ ((i : (Module.rank F E).ord.ToType) → Field.Emb.Cardinal.factor ↑i)

A bijection between E →ₐ[F] Ē and the product of E⟮<i⁺⟯ →ₐ[E⟮<i⟯] Ē over all i : ι.

Defined in: Mathlib.FieldTheory.CardinalEmb
Cited by: 1 results in Mathlib
Foundations: Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Fact Algebra.IsAlgebraic

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Cites35

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

DFunLike.coeproof · cited by 62,936
Algebrastatement and proof · cited by 11,388
Top.topproof · cited by 9,680
Equivstatement and proof · cited by 8,337
Fieldstatement and proof · cited by 7,404
WithTopproof · cited by 3,754
Equiv.symmproof · cited by 3,681
AlgHomproof · cited by 3,236
Factstatement and proof · cited by 2,726
Cardinalstatement · cited by 2,598
WithTop.somestatement and proof · cited by 1,128
Cardinal.aleph0statement and proof · cited by 521

Cited by1

Results whose statement or proof uses this declaration.

Field.Emb.cardinal_eq_two_pow_rankproof · cited by 2