Theorems · Theorem · commutative algebra
Algebra.WeaklyQuasiFiniteAt.of_surjectiveOnStalks
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : CommRing T] [inst_4 : Algebra R T] (p : Ideal S) [inst_5 : p.IsPrime] [Algebra.WeaklyQuasiFiniteAt R p]
(q : Ideal T) [inst_7 : q.IsPrime] (f : S →ₐ[R] T),
f.SurjectiveOnStalks → p = Ideal.comap f q → Algebra.WeaklyQuasiFiniteAt R qUse Algebra.QuasiFiniteAt.of_surjectiveOnStalks instead for Algebra.QuasiFiniteAt R p.
- Defined in
- Mathlib.RingTheory.QuasiFinite.Weakly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AlgHomstatement and proof · cited by 3,236
- Ideal.IsPrimestatement and proof · cited by 827
- AlgHom.toRingHomstatement and proof · cited by 490
- Ideal.comapstatement and proof · cited by 443
- RingHom.SurjectiveOnStalksstatement and proof · cited by 26
- Algebra.WeaklyQuasiFiniteAtstatement and proof · cited by 18
- Localization.localAlgHomproof · cited by 6
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1