Theorems · Theorem · field theory
exists_isTranscendenceBasis_subset
∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [NoZeroDivisors A]
[FaithfulSMul R A] (s : Set A) [Algebra.IsAlgebraic (↥(Algebra.adjoin R s)) A],
∃ t ⊆ s, IsTranscendenceBasis R Subtype.val- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Subalgebrastatement · cited by 1,353
- NoZeroDivisorsstatement and proof · cited by 545
- Algebra.adjoinstatement and proof · cited by 535
- FaithfulSMulstatement and proof · cited by 340
- Algebra.IsAlgebraicstatement and proof · cited by 322
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- IsTranscendenceBasisstatement and proof · cited by 74
- Set.empty_subsetproof · cited by 70
- algebraicIndependent_empty_iffproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- exists_isTranscendenceBasis_and_isSeparable_of_perfectFieldproof · cited by 0