Theorems · Theorem · field theory
Field.fg_iff_essFiniteType
∀ {F : Type u_1} [inst : Field F], Field.FG F ↔ Algebra.EssFiniteType (↥⊥) FA field is finitely generated if and only if it is essentially of finite type over its prime subfield.
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- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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- Fieldstatement and proof · cited by 7,404
- Bot.botstatement · cited by 4,720
- Subfieldstatement · cited by 303
- Algebra.EssFiniteTypestatement · cited by 68
- Field.FGstatement · cited by 4
- IntermediateField.fg_top_iffproof · cited by 2
- Field.fg_iff_fg_top_botproof · cited by 1
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