Theorems · Theorem · algebraic geometry
PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalks_aux
∀ (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],
(algebraMap R T).SurjectiveOnStalks →
∀ (p₁ p₂ : PrimeSpectrum (TensorProduct R S T)),
PrimeSpectrum.tensorProductTo R S T p₁ = PrimeSpectrum.tensorProductTo R S T p₂ → p₁ ≤ p₂- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomproof · cited by 10,189
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- TensorProductstatement and proof · cited by 2,545
- TensorProduct.tmulproof · cited by 1,182
- PrimeSpectrumstatement and proof · cited by 625
- AlgHom.toRingHomproof · cited by 490
- Ideal.primeComplproof · cited by 462
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isEmbedding_tensorProductTo_of_surjectiveOnStalksproof · cited by 1