Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.finite_primesOver
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.QuasiFinite R S] (I : Ideal R), (I.primesOver S).Finite- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Set.Finitestatement and proof · cited by 1,814
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrum.asIdealproof · cited by 333
- Set.Finite.subsetproof · cited by 285
- Ideal.LiesOverproof · cited by 272
- Ideal.underproof · cited by 170
- Set.Finite.imageproof · cited by 96
- Ideal.primesOverstatement and proof · cited by 84
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.ncard_primesOver_mul_ramificationIdxIn_mul_inertiaDegInproof · cited by 5