Theorems · Theorem · commutative algebra
Algebra.WeaklyQuasiFiniteAt.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.WeaklyQuasiFiniteAt 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.WeaklyQuasiFiniteAt A qUse Algebra.QuasiFiniteAt.baseChange instead for Algebra.QuasiFiniteAt R p.
- Defined in
- Mathlib.RingTheory.QuasiFinite.Weakly
- Cited by
- 2 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.
Cites63
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
- Semiringproof · cited by 13,802
- 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
- Bot.botproof · cited by 4,720
- Algebra.algebraMapproof · cited by 4,706
- AlgHomproof · cited by 3,236
- TensorProductstatement and proof · cited by 2,545
- HasQuotient.Quotientproof · cited by 2,301
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.not_weaklyQuasiFiniteAtproof · cited by 2
- Polynomial.not_ker_le_map_C_of_surjective_of_weaklyQuasiFiniteAtproof · cited by 1