Theorems · Theorem · commutative algebra

RingCon.ker_eq_lift_of_injective

∀ {M : Type u_1} {P : Type u_3} [inst : NonAssocSemiring M] [inst_1 : NonAssocSemiring P] {c : RingCon M} {f : M →+* P}
  (H : c ≤ RingCon.ker f), Function.Injective ⇑(c.lift f H) → RingCon.ker f = c

Given a ring homomorphism f from M to P, the kernel of f is the unique ring congruence relation on M whose induced map from the quotient of M to P is injective.

Defined in

Mathlib.RingTheory.Congruence.Hom

Cited by

0 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Quot.sound

Assumes

NonAssocSemiringNonAssocSemiring