Theorems · Theorem · commutative algebra
RingHom.kerLift_injective
∀ {R : Type u} {S : Type v} [inst : Ring R] [inst_1 : Semiring S] (f : R →+* S), Function.Injective ⇑f.kerLiftThe induced map from the quotient by the kernel is injective.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Semiringstatement and proof · cited by 13,802
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Idealstatement · cited by 4,748
- HasQuotient.Quotientstatement · cited by 2,301
- le_rflproof · cited by 1,558
- RingHom.kerstatement and proof · cited by 363
- RingHom.kerLiftstatement · cited by 13
- RingHom.lift_injective_of_ker_le_idealproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Ideal.kerLiftAlg_injectiveproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.Spec_iffproof · cited by 1
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1
- AlgebraicGeometry.specTargetImageFactorization_app_injectiveproof · cited by 0