Theorems · Theorem · commutative algebra
Algebra.QuasiFiniteAt.baseChange
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal S)
[inst_3 : p.IsPrime] [Algebra.QuasiFiniteAt R p] {A : Type u_4} [inst_5 : CommRing A] [inst_6 : Algebra R A]
(q : Ideal (TensorProduct R A S)) [inst_7 : q.IsPrime],
p = Ideal.comap Algebra.TensorProduct.includeRight.toRingHom q → Algebra.QuasiFiniteAt A q- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 4 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.
Cites42
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
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- map_oneproof · cited by 861
- Ideal.IsPrimestatement and proof · cited by 827
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Ideal.exists_not_mem_forall_mem_of_ne_of_liesOverproof · cited by 1
- Algebra.quasiFiniteAt_iff_isOpen_singleton_fiberproof · cited by 1
- Ideal.Fiber.lift_residueField_surjectiveproof · cited by 1