Theorems · Theorem · commutative algebra
RingHom.flat_algebraMap_iff
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S],
(algebraMap R S).Flat ↔ Module.Flat R S- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebra.algebraMapstatement and proof · cited by 4,706
- Module.Flatstatement and proof · cited by 279
- RingHom.Flatstatement · cited by 60
- toAlgebra_algebraMapproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.FaithfullyFlat.iff_flat_and_comap_surjectiveproof · cited by 5
- RingHom.Flat.isStableUnderBaseChangeproof · cited by 1
- RingHom.Flat.holdsForLocalizationAwayproof · cited by 1
- RingHom.Flat.of_isFieldproof · cited by 0