Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.eq_of_le_of_under_eq
∀ {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 Q : Ideal S) [P.IsPrime] [Q.IsPrime], P ≤ Q → Ideal.under R P = Ideal.under R Q → P = Q- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.comapproof · cited by 443
- PrimeSpectrum.asIdealproof · cited by 333
- Ideal.understatement and proof · cited by 170
- PrimeSpectrum.extproof · cited by 43
- Algebra.QuasiFinitestatement and proof · cited by 28
- Algebra.QuasiFinite.isDiscrete_comap_preimage_singletonproof · cited by 2
- IsDiscrete.eq_of_specializesproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.QuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 1