Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.finite_comap_preimage_singleton
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.QuasiFinite R S] (P : PrimeSpectrum R), (PrimeSpectrum.comap (algebraMap R S) ⁻¹' {P}).Finite- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.preimagestatement · cited by 4,946
- Algebra.algebraMapstatement · cited by 4,706
- Set.Finitestatement · cited by 1,814
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.comapstatement · cited by 199
- Algebra.QuasiFinitestatement and proof · cited by 28
- Equiv.finite_iffproof · cited by 21
- PrimeSpectrum.preimageEquivFiberproof · cited by 8
- finite_of_compact_of_discreteproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.QuasiFinite.iff_finite_comap_preimage_singletonproof · cited by 4
- Algebra.QuasiFinite.finite_comap_preimageproof · cited by 1
- Algebra.QuasiFinite.finite_primesOverproof · cited by 1