Theorems · Theorem · commutative algebra
Algebra.WeaklyQuasiFiniteAt.of_algHom_localization
∀ {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 : Localization.AtPrime p →ₐ[R] Localization.AtPrime q),
Function.Surjective ⇑f → Algebra.WeaklyQuasiFiniteAt R qUse Algebra.QuasiFinite.of_surjective_algHom instead for Algebra.QuasiFiniteAt R p.
- Defined in
- Mathlib.RingTheory.QuasiFinite.Weakly
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- le_reflproof · cited by 2,061
- IsUnitproof · cited by 1,602
- RingHom.compproof · cited by 899
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapproof · cited by 692
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.of_surjectiveOnStalksproof · cited by 1