Theorems · Theorem · algebraic geometry
Algebra.not_isStronglyTranscendental_of_quasiFiniteAt
∀ {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.QuasiFiniteAt R P], ¬IsStronglyTranscendental R x[Stacks Tag 00Q2](https://stacks.math.columbia.edu/tag/00Q2)
- Defined in
- Mathlib.RingTheory.ZariskisMainTheorem
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- Polynomialstatement · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement and proof · cited by 827
- Polynomial.aevalstatement and proof · cited by 615
- AlgHom.toRingHomstatement and proof · cited by 490
- IsReducedstatement and proof · cited by 98
- RingHom.Finitestatement and proof · cited by 48
- Algebra.QuasiFiniteAtstatement and proof · cited by 29
- IsStronglyTranscendentalstatement · cited by 14
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1
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