Theorems · Definition · commutative algebra

RingCon.kerLift

{M : Type u_1} →
  {P : Type u_3} →
    [inst : NonAssocSemiring M] → [inst_1 : NonAssocSemiring P] → (f : M →+* P) → (RingCon.ker f).Quotient →+* P

The homomorphism induced on the quotient of a ring by the kernel of a ring homomorphism.

Defined in: Mathlib.RingTheory.Congruence.Hom
Cited by: 5 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Quot.sound
Assumes: NonAssocSemiring NonAssocSemiring

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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

RingHomstatement and proof · cited by 10,189
NonAssocSemiringstatement and proof · cited by 805
RingCon.Quotientstatement · cited by 118
RingCon.kerstatement and proof · cited by 47
RingCon.liftproof · cited by 16

Cited by7

Results whose statement or proof uses this declaration.

RingCon.quotientKerEquivRangeSproof · cited by 1
RingCon.kerLift_injectivestatement · cited by 1
RingCon.quotientKerEquivOfRightInverseproof · cited by 1
RingCon.rangeS_kerLiftstatement · cited by 0
RingCon.kerLift_mkstatement · cited by 0
RingCon.kerLift_range_eqstatement · cited by 0
RingCon.quotientKerEquivOfRightInverse_applystatement · cited by 0