Theorems · Theorem · field theory
RatFunc.Luroth.eq_adjoin_generator
∀ {K : Type u_1} [inst : Field K] {E : IntermediateField K (RatFunc K)}, E = K⟮RatFunc.Luroth.generator E⟯Lüroth's theorem. Any intermediate field between K and K⟮X⟯ is
generated by a single element generator E. See also transcendental_generator
for the statement that the generator is transcendental if E ≠ ⊥.
- Defined in
- Mathlib.FieldTheory.RatFunc.Luroth
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites18
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- Fieldstatement and proof · cited by 7,404
- Bot.botproof · cited by 4,720
- le_antisymmproof · cited by 2,068
- Polynomial.natDegreeproof · cited by 1,105
- IntermediateFieldstatement and proof · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- RatFuncstatement and proof · cited by 301
- RatFunc.Luroth.generatorstatement and proof · cited by 11
- mul_eq_right₀proof · cited by 7
- RatFunc.Luroth.generator_ne_Cproof · cited by 3
- IntermediateField.adjoin_zeroproof · cited by 3
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