Theorems · Theorem · field theory
IntermediateField.transcendental_adjoin_iff
∀ {F : Type u_2} {E : Type u_3} {S : Type u_5} {s : Set E} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
[inst_3 : Ring S] [inst_4 : Algebra E S] {x : S},
Transcendental (↥(IntermediateField.adjoin F s)) x ↔ Transcendental (↥(Algebra.adjoin F s)) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Subalgebrastatement · cited by 1,353
- IntermediateFieldstatement · cited by 988
- Algebra.adjoinstatement and proof · cited by 535
- IntermediateField.adjoinstatement and proof · cited by 382
- Transcendentalstatement · cited by 91
- Algebra.IsAlgebraic.transcendental_iffproof · cited by 1
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