Theorems · Theorem · field theory
exists_isTranscendenceBasis
∀ (R : Type u_1) (A : Type w) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [FaithfulSMul R A], ∃ s, IsTranscendenceBasis R Subtype.val
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- FaithfulSMulstatement and proof · cited by 340
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
- IsTranscendenceBasisstatement and proof · cited by 74
- algebraicIndependent_empty_iffproof · cited by 2
- exists_isTranscendenceBasis_supersetproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- finTrdeg_iff_trdegproof · cited by 4
- lift_trdeg_add_eqproof · cited by 2
- IsAlgClosed.ringEquiv_of_equiv_of_charZeroproof · cited by 1
- exists_isTranscendenceBasis'proof · cited by 1
- exists_finset_isTranscendenceBasisproof · cited by 0