Theorems · Definition · commutative algebra
RingHom.ContainsIdentities
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) → PropA property P of ring homs is said to contain identities if P holds
for the identity homomorphism of every ring.
- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
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.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
Cited by12
Results whose statement or proof uses this declaration.
- RingHom.HoldsForLocalizationAway.containsIdentitiesstatement · cited by 1
- RingHom.IsPurelyInseparable.containsIdentitiesstatement · cited by 0
- RingHom.Flat.containsIdentitiesstatement · cited by 0
- RingHom.Etale.containsIdentitiesstatement · cited by 0
- RingHom.IsStandardOpenImmersion.containsIdentitiesstatement · cited by 0
- RingHom.Bijective.containsIdentitiesstatement · cited by 0
- AlgebraicGeometry.HasRingHomProperty.isMultiplicativestatement and proof · cited by 0
- RingHom.PropertyIsLocal.HoldsForLocalizationAwaystatement and proof · cited by 0
- AlgebraicGeometry.HasAffineProperty.affineAnd_containsIdentitiesstatement and proof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.of_isOpenImmersionstatement and proof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.containsIdentitiesstatement and proof · cited by 0
- RingHom.finite_containsIdentitiesstatement · cited by 0