Theorems · Theorem · field theory
IsTranscendenceBasis.algebraMap_comp
∀ {ι : Type u} {R : Type u_1} {S : Type v} {A : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing A]
[inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] [Nontrivial R]
[NoZeroDivisors S] [Algebra.IsAlgebraic S A] [FaithfulSMul S A] {x : ι → S},
IsTranscendenceBasis R x → IsTranscendenceBasis R (⇑(algebraMap S A) ∘ x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangeproof · cited by 4,705
- IsScalarTowerstatement and proof · cited by 3,896
- AlgHomproof · cited by 3,236
- Nontrivialstatement and proof · cited by 2,416
- AlgEquivproof · cited by 1,681
- Subalgebraproof · cited by 1,353
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