Theorems · Theorem · commutative algebra
Module.algebraMap_surjective_of_rankAtStalk_le_one
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Flat R S]
[Module.Finite R S], (∀ (p : PrimeSpectrum R), Module.rankAtStalk S p ≤ 1) → Function.Surjective ⇑(algebraMap R S)- Defined in
- Mathlib.RingTheory.Flat.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 122 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.
- DFunLike.coestatement and proof · cited by 62,936
- Moduleproof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupproof · cited by 12,871
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Cardinalproof · cited by 2,598
- TensorProductproof · cited by 2,545
- Module.Finitestatement and proof · cited by 1,032
- PrimeSpectrumstatement and proof · cited by 625
Cited by1
Results whose statement or proof uses this declaration.
- Module.Flat.tfae_algebraMap_surjectiveproof · cited by 1