Theorems · Theorem · commutative algebra
Algebra.QuasiFiniteAt.of_surjectiveOnStalks
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] (p : Ideal S) [inst_5 : p.IsPrime] [Algebra.QuasiFiniteAt R p]
(f : S →ₐ[R] T),
f.SurjectiveOnStalks → ∀ (q : Ideal T) [inst_7 : q.IsPrime], p = Ideal.comap f.toRingHom q → Algebra.QuasiFiniteAt R q- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 3 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.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- CommSemiringproof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- FunLikeproof · cited by 2,560
- Ideal.IsPrimestatement and proof · cited by 827
- RingHomClass.toRingHomproof · cited by 746
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Algebra.WeaklyQuasiFiniteAt.of_restrictScalarsproof · cited by 1
- Algebra.QuasiFiniteAt.of_surjectiveOnStalks_of_liesOverproof · cited by 0