Theorems · Theorem · commutative algebra
RingHom.kerLift_mk
∀ {R : Type u} {S : Type v} [inst : Ring R] [inst_1 : Semiring S] (f : R →+* S) (r : R),
f.kerLift ((Ideal.Quotient.mk (RingHom.ker f)) r) = f r- Cited by
- 4 results in Mathlib
- Foundations
- Depth 85 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 · 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
- Ideal.Quotient.mkstatement · cited by 610
- RingHom.kerstatement and proof · cited by 363
- RingHom.kerLiftstatement · cited by 13
- Ideal.Quotient.lift_mkproof · cited by 9
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.iff_comp_injective_of_smallproof · cited by 4
- Algebra.trace_quotient_eq_of_isDedekindDomainproof · cited by 3
- trace_quotient_eq_trace_localization_quotientproof · cited by 1
- Algebra.FormallySmooth.liftOfSurjective_applyproof · cited by 1