Theorems · Theorem · field theory
IntermediateField.algebraicIndependent_adjoin_iff
∀ {ι : Type u_1} {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 : CommRing S] [inst_4 : Algebra E S] {x : ι → S},
AlgebraicIndependent (↥(IntermediateField.adjoin F s)) x ↔ AlgebraicIndependent (↥(Algebra.adjoin F s)) x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 143 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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- 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
- AlgebraicIndependentstatement · cited by 120
- Algebra.IsAlgebraic.algebraicIndependent_iffproof · cited by 2
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