Theorems · Theorem · field theory
AlgebraicIndependent.isTranscendenceBasis_of_lift_trdeg_le
∀ {ι : Type u} {R : Type u_1} {A : Type w} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Nontrivial R] [NoZeroDivisors A],
AlgebraicIndependent R x →
Algebra.trdeg R A < Cardinal.aleph0 →
Cardinal.lift.{u, w} (Algebra.trdeg R A) ≤ Cardinal.lift.{w, u} (Cardinal.mk ι) → IsTranscendenceBasis R x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 146 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Cardinalstatement · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- NoZeroDivisorsstatement and proof · cited by 545
- Cardinal.aleph0statement and proof · cited by 521
- FaithfulSMulproof · cited by 340
- LE.le.trans_eqproof · cited by 328
- AlgebraicIndependentstatement and proof · cited by 120
- Cardinal.lift_leproof · cited by 78
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicIndependent.isTranscendenceBasis_of_lift_trdeg_le_of_finiteproof · cited by 1
- AlgebraicIndependent.isTranscendenceBasis_of_trdeg_leproof · cited by 0