Theorems · Theorem · commutative algebra
RingHom.Flat.id
∀ (R : Type u_1) [inst : CommRing R], (RingHom.id R).Flat
The identity of a ring is flat.
- Defined in
- Mathlib.RingTheory.RingHom.Flat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- RingHom.Flatstatement · cited by 60
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIsoproof · cited by 1
- RingHom.Flat.containsIdentitiesproof · cited by 0