Theorems · Theorem · field theory
AlgebraicIndependent.isTranscendenceBasis_of_trdeg_le
∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] [Nontrivial R]
[NoZeroDivisors A] {ι : Type w} {x : ι → A},
AlgebraicIndependent R x →
Algebra.trdeg R A < Cardinal.aleph0 → Algebra.trdeg R A ≤ Cardinal.mk ι → IsTranscendenceBasis R x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
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 and proof · cited by 2,598
- Nontrivialstatement and proof · cited by 2,416
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftproof · cited by 583
- NoZeroDivisorsstatement and proof · cited by 545
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.lift_idproof · cited by 163
- AlgebraicIndependentstatement and proof · cited by 120
- IsTranscendenceBasisstatement · cited by 74
- Algebra.trdegstatement and proof · cited by 39
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