Theorems · Theorem · algebraic geometry
Ideal.Fiber.exists_smul_eq_one_tmul
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (p : Ideal R)
[inst_3 : p.IsPrime] (x : p.Fiber S), ∃ r ∉ p, ∃ s, r • x = 1 ⊗ₜ[R] s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- Idealstatement and proof · cited by 4,748
- TensorProduct.tmulstatement and proof · cited by 1,182
- Ideal.IsPrimestatement and proof · cited by 827
- AlgEquiv.symmproof · cited by 615
- map_smulproof · cited by 566
- Ideal.primeComplstatement · cited by 462
- Localization.AtPrimestatement · cited by 299
- Ideal.ResidueFieldstatement and proof · cited by 119
- Ideal.Fiberstatement and proof · cited by 40
Cited by3
Results whose statement or proof uses this declaration.
- Ideal.exists_not_mem_forall_mem_of_ne_of_liesOverproof · cited by 1
- Algebra.IsUnramifiedAt.exists_notMem_forall_ne_mem_and_adjoin_eq_topproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueFieldproof · cited by 1