Theorems · Theorem · commutative algebra
RingCon.kerLift_injective
∀ {M : Type u_1} {P : Type u_3} [inst : NonAssocSemiring M] [inst_1 : NonAssocSemiring P] (f : M →+* P),
Function.Injective ⇑(RingCon.kerLift f)A ring homomorphism f induces an injective homomorphism on the quotient by f's kernel.
- Defined in
- Mathlib.RingTheory.Congruence.Hom
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- NonAssocSemiringstatement and proof · cited by 805
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- RingCon.Quotientstatement · cited by 118
- RingCon.kerstatement · cited by 47
- RingCon.kerLiftstatement · cited by 5
- AddCon.kerLift_injectiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- RingCon.kerLiftₐ_injectiveproof · cited by 0