Theorems · Theorem · commutative algebra
IsStronglyTranscendental.iff_of_isFractionRing
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (K : Type u_4)
[inst_3 : Field K] [inst_4 : Algebra R K] [inst_5 : Algebra S K] [IsScalarTower R S K] [FaithfulSMul R S]
[IsFractionRing S K] {x : S}, IsStronglyTranscendental R x ↔ Transcendental R ((algebraMap S K) x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- le_rflproof · cited by 1,558
- IsFractionRingstatement and proof · cited by 738
- FaithfulSMulstatement and proof · cited by 340
- Transcendentalstatement and proof · cited by 91
- IsStronglyTranscendentalstatement · cited by 14
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