Theorems · Theorem · algebraic geometry
Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAt
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [IsReduced S] {x : S},
(Polynomial.aeval x).Finite →
∀ (P : Ideal S) [inst_4 : P.IsPrime] [Algebra.WeaklyQuasiFiniteAt R P], ¬IsStronglyTranscendental R x- Defined in
- Mathlib.RingTheory.ZariskisMainTheorem
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites81
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Polynomialstatement and proof · cited by 5,681
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- AlgHomproof · cited by 3,236
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.not_isStronglyTranscendental_of_quasiFiniteAtproof · cited by 0