Theorems · Theorem · commutative algebra
Algebra.QuasiFiniteAt.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] {P Q : Ideal S}
[P.IsPrime] [inst_4 : Q.IsPrime], P ≤ Q → Ideal.under R P = Ideal.under R Q → ∀ [Algebra.QuasiFiniteAt R Q], P = Q- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.mapproof · cited by 692
- Localization.AtPrimeproof · cited by 299
- IsLocalRing.maximalIdealproof · cited by 297
- Ideal.understatement and proof · cited by 170
- Algebra.QuasiFiniteAtstatement and proof · cited by 29
- Localization.AtPrime.under_maximalIdealproof · cited by 9
- Ideal.under_underproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 0