Theorems · Theorem · field theory

Algebra.finite_of_essFiniteType_of_isAlgebraic

∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] [Algebra.EssFiniteType F E]
  [Algebra.IsAlgebraic F E], Module.Finite F E

Defined in: Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra
Cited by: 1 results in Mathlib
Foundations: Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field Field Algebra Algebra.EssFiniteType Algebra.IsAlgebraic

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Cites16

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

Finsetproof · cited by 13,712
Algebrastatement and proof · cited by 11,388
Top.topproof · cited by 9,680
SetLike.coeproof · cited by 8,199
Fieldstatement and proof · cited by 7,404
Subalgebraproof · cited by 1,353
Module.Finitestatement · cited by 1,032
IntermediateField.adjoinproof · cited by 382
Algebra.IsAlgebraicstatement and proof · cited by 322
Algebra.FiniteTypeproof · cited by 84
Algebra.EssFiniteTypestatement and proof · cited by 68
Algebra.IsAlgebraic.isAlgebraicproof · cited by 51

Cited by1

Results whose statement or proof uses this declaration.

IntermediateField.exists_finset_maximalFor_isTranscendenceBasis_separableClosureproof · cited by 1